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]]>It is important to study this topic well because questions from it definitely appear on the JEE. Comprehension type questions from this topic are common too. Also, complex questions can be formed when rotational mechanics is combined with other concepts such as electromagnetism, SHM, etc.
To excel in rotational mechanics for IIT JEE Physics, you need to put in a great amount of time and effort. So let’s start by looking at some of the core concepts.
When you hear the term “rigid body”, what comes to mind? Well, when I first heard this word I thought it was some object which was very tough to deform–something very hard and “rigid”. I didn’t know that this simple thing was an incredibly importance concept of JEE rotational mechanics! Why is it so important? Because learning the rotational mechanics of a rigid body is much simpler than a non-rigid body. You see, the rotational mechanics of a non-rigid body is very complex–and not necessary for the JEE!
So what exactly is a “rigid body?” It is basically a system of particles where the distance/separation between each pair of particles remains constant (with respect to time). So it means that the shape and size hardly change during the motion. For every pair of particles in a rigid body, there is zero velocity of separation or approach. Hence, we can say that the deformation of a rigid body during motion is almost zero. A ball bearing made of hardened steel is a good example of a rigid body.
In real life, there are no rigid bodies. They are an assumption made in classical mechanics. This assumption makes the calculations related to the movement of bodies easier. However, in quantum mechanics, point masses (molecules) are often seen as rigid bodies.
Well, now that we know what a rigid body is, let’s study the kinds of motion they can perform. As per the JEE syllabus, we need to learn Translation and Rotation. Let’s just stick to only these two types of rigid body motion.
Suppose that the car (shown below) is a rigid body and is moving from left to right.
This is a case of pure translation. No rotation is happening here. In a pure translation of a rigid body, the velocity and acceleration of each and every particle of the rigid body is same.
This fact can be visualized better if we think of its opposite. So suppose some particles of the car have a greater velocity or acceleration than the remaining particles. The faster particles would move farther and the car would be dismantled. Just imagine the seat of the car having a faster velocity than the remaining parts of the car. Sounds funny, right?
In translation, all the particles of the rigid body move along parallel paths, and if these parallel paths are straight lines, the motion is said to be a rectilinear translation.
Consider the image below in which a rod is rotated around a fixed point O.
If you notice, during the course of one full rotation, the part of the rod at point O remains fixed. However, the tip of the rod farthermost to point O covers the greatest distance (2𝛑l, where l is the length of the rod). Hence, as you can see, the different points of the rod have a different velocity. One very important point to notice here is that all the points on the rod move in concentric circular paths only.
A rigid body is considered to be in pure rotation only if each and every particle of the body moves in a circle, and the centers of all the circles lie on a straight line. This line is known as the axis of rotation (A.O.R.). In pure rotation, all points in the rigid body that are perpendicular to the A.O.R. turn through the same angle in the same interval. In the figure above, the A.O.R. would be the Z axis.
General rigid body motion is a combination of pure translation and pure rotation. So, while solving a rotational mechanics question, try to break the motion of the body into translation and rotation, then solve for each of them.
Have you ever rotated a ball tied to a thread? Think of swinging it in a circular motion above your head. I know, it’s hard to see a connection between concepts in the JEE syllabus and your daily life! But I’m sure we can all imagine swinging a ball tied to a thread. As we spin this ball around, we can observe the fundamentals of angular velocity!
While rotating the ball, if the string is suddenly cut, in which direction will the ball go? Will it still try to complete the circle or will it go tangentially? With what velocity will it go? Is there some relation between the rate of change in the angle subtended at the centre (at the point where you’re holding the string), and the velocity with which the ball goes away when the string is cut suddenly?
We’ll learn the answer to all these questions right here!
Consider the figure below. Notice how the circular motion in the picture is happening in a horizontal plane. A circular motion happening in a vertical plane is an altogether different ball game!
In the figure above, the angle θ is known as angular displacement. It is basically the angle covered with respect to a baseline when an object rotates on an axis. The angular displacement happens on the same plane as that of the rotation of the object.
Angular velocity (ω) is the rate of change of angular displacement. Depending on the time frame chosen to calculate the rate of change of angular displacement, angular velocity can be of one of the following two types.
Angular velocity can be thought of as a vector quantity. The direction of ω is obtained using right-hand thumb rule — curl up your fingers of the right hand in a manner that the direction of the curl is in the direction of the sense of rotation. Your extended thumb will then give the direction of the angular velocity ω.
The unit of angular velocity is rad/s or radians per second.
The v mentioned in Figure 3 is known as tangential velocity. It is the linear velocity of the particle that is performing a circular motion and is directed along the tangent to the circular path at the given point at that particular instant. It is the initial velocity with which the ball will fall off if the ball is at point P of the circular path (shown in Figure 3) and the string is cut immediately.
The relationship between v, ω, and r is:
v = ω × r
Let’s strengthen the concepts we learned above by solving a problem!
Question: If a stone is rotating in a circle of diameter 10m with velocity 20m/s, find the angular velocity of the stone.
Solution:
v = ω r
So, ω = v/r
r = 10/2 = 5m and v = 20m/s
Hence, ω = 20/5 = 4 s^{-1} or 4 Hz
Answer: b)
Please note that 1 Hz = 2𝜋 rad/s
In the previous section, we learned about Angular Velocity. Now, let’s talk about the rate of change of Angular Velocity, also known as Angular Acceleration, often denoted by 𝛂.
Consider the merry-go-round in the figure below. When there’s no one around, the merry-go-round is in a state of rest. Suddenly, the children decide they want to enjoy a ride on the merry-go-round. They select one of their friends (the little girl in the red shirt) and ask her to rotate the merry-go-round fast. She puts in her energy and rotates it hard. The merry-go-round, which was earlier at rest, is now rotating faster and faster (about its centre, of course). The angular velocity (ω) of each point of the merry-go-round is increasing. The merry-go-round not only has Angular Velocity, but also Angular Acceleration. That is the reason for the increasing ω of the merry-go-round.
Depending on the time frame chosen to calculate the rate of change of angular velocity, angular acceleration can be of one of the following two types:
The unit of angular acceleration is rad/s^{2} or radians per second squared. The angular acceleration is also a vector quantity. Its direction can be along the direction of angular velocity or opposite to it.
We learned how to find the direction of the angular velocity vector in the previous section using the right-hand thumb rule. If the magnitude of angular velocity ω is increasing, the direction of angular acceleration 𝛼 is along the direction of ω. If the magnitude of ω is decreasing, the direction of angular acceleration 𝛼 is opposite to the direction of ω.
Let’s strengthen our understanding of angular acceleration and angular velocity by solving a problem here!
Question: Suppose when you increase the speed of your room fan from medium to high, the blades accelerate at 1.2 rad/s^{2} for 1.5 seconds. Assume the initial angular speed of the fan blades to be equal to 3.0 rad/s, find the final angular speed of the fan blades in rad/s.
a.) 4.8 rad/s
b.) 9.6 rad/s
c.) 10.0 rad/s
d.) 2.4 rad/s
Solution:
𝛼 = (𝛥ω)/(𝛥t)
𝛥ω = ωfinal – ωinitial
Hence, 𝛼 = (ωfinal – ωinitial)/(𝛥t)
Thus, ωfinal = ωinitial + 𝛼(𝛥t)
=> ωfinal = 3.0 + (1.2*1.5) = 4.8 rad/s
Answer: a)
In this post, we discussed the fundamentals of rotation mechanics, which are very important in building the foundation to a great understanding of the topic. Hope you found it useful!
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]]>It is both fascinating and frustrating that scientists are always using words derived from different languages. The deeper you dive into the sciences, more you come across Greek and Latin. So the beginning of the word, ‘kinemat-‘ is Greek and means ‘motion’. The end of the word, ‘ics’ is Latin and means ‘the study of’. Therefore, kinematics is ‘the study of motion’. So, Kinematics is the study the motion of objects and groups of objects without considering the mass or the forces that caused the motion.
Kinematics is a part of mechanics and lies at the heart of physics. It fascinates me because if we know the present condition of an object, we can predict its future. We can get the answer to many questions like how far an object will travel or in which direction will it move or how quickly it can go from a dead stop to full speed.
In the JEE Main and JEE Advanced, the Kinematics plays an important role. Every year, more than ten questions are asked from mechanics. About 2 – 3 questions are solely based from this chapter, and the rest cannot be solved without a working knowledge of kinematics.
Kinematics will become a nightmare if the basics are not clear to you. So, start from the basics. Don’t get overwhelmed at this point–just get started.
To start with the absolute basics, one can read NCERT thoroughly. The point of this blog is to highlight all the essential concepts, address common mistakes, address previous years’ questions related to Kinematics, and to make sure that you score better marks in the JEE Advanced. The concepts given here are in concise form and can be used for revision before the examination.
Resnick Halliday is an excellent book for theory. You can also buy Arihant books for Mechanics. They contain tons of problems and a lot of tips and tricks. Finally, to become unbeatable in Mechanics, solve Irodov. Trust me this book has a lot of challenging problems. After solving all the problems, you can easily crack the physics olympiad.
According to NCERT, the following topics come under Kinematics:
Now let’s see some theory.
Rectilinear motion is the motion along a straight line or in one dimension. It deals with the kinematics of particle in one dimension. Now read and understand the following definitions:
One of the essential aspects of Kinematics is the study of graphs. Study the following graphs.
Important Points that you should keep a note of:
Some important formulae for Uniformly Accelerated Motion:
Be careful while applying these formulas. Maintaining proper sign convection is an absolute must. These formulae should be remembered by heart because they help in time management.
Some Formulas for Non-Uniformly Accelerated Motion:
Projectile motion is a form of motion experienced by an object or particle (a projectile) that is thrown near the Earth’s surface and moves along a curved path under the action of gravity.
Source:https://calculator.tutorvista.com/trajectory-calculator.html
Here v_{x} is the velocity along the x-axis, u_{x} is the initial velocity along the x-axis, v_{y} is the velocity along the y-axis, u_{y} is the initial velocity along the y-axis, g is the acceleration due to gravity, t is the time taken.
u is the initial Velocity, sin θ is the component along the y-axis, and cos θ is the component along the x-axis.
Now let us derive the equation of trajectory of a projectile motion.
We know:
x = u_{x}t = u cosθ t
y = u_{y}t – 0.5gt^{2} = u sinθ t – 0.5gt^{2}
Eliminating t from both the equations, we get:
Till now we’ve seen ground to ground projections, but a projectile can be launched from an inclined plane also.
If we continue to use the natural axis system, it becomes tedious. So, to simplify our task we adopt a new axis system, that is–x-axis along the plane and the y-axis perpendicular to the plane.
In the case of projection on an inclined plane, remembering formulas can be a tough task. So, it’s advisable to solve problems by breaking down vectors along–and perpendicular to–the plane and apply formulas of rectilinear motion. One should not be afraid to play with vectors.
When a particle moves in a plane such that its distance from a fixed point remains constant, then its motion is called circular motion with respect to that fixed point.
Read and get a grasp of the following definitions:
Centripetal and Centrifugal Force
Here V is the tangential velocity, r is the radius of the circle, w is the angular velocity, a is the centripetal acceleration, and F is the centripetal force acting on the particle. Now let us see some relation among angular variables.
Any curved path can be assumed to be made of infinite circular arcs. The radius of curvature at a point is the radius of the circular arc at a particular point which fits the curve at that point.
F_{c} = mv^{2}/R
=> R = mv^{2}/F_{c}
Here R is the radius of the curvature. If the equation of trajectory of a particle is given, we can find the radius of curvature of the instantaneous circle by using this formula.
Only the theory won’t help, so solve the list of the following problems for better understanding.
Relative motion of an object with respect to the observer is defined as the motion with which the object appears to move if the observer is considered to be at rest. The concept of relative motion is introduced to simplify solving problems. No new theory is taught. The only way to master the concept of relative motion is to solve as many problems as possible. Some important problem types are listed below:
The best thing would be first to classify the chapter into such profiles and identify which profile you are weak at. After doing this, you can start reading theory for the profile and simultaneously solve related questions. Put this philosophy to the test. You will be surprised at how much better you understand the concepts. And how much better you will do on your exams.
I hope this post will help you grasp a firm command over mechanics.
All the best!
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]]>The post Modern Physics for JEE appeared first on Magoosh JEE Blog.
]]>I can tell you, one can complete the whole Modern Physics JEE course in just a month or less than that, depending on how much time he/she is putting in every day. It is a scoring topic and requires less efforts compared to other chapters. First things first, what’s the syllabus?
The syllabus includes all of the following:
This is the only topic which will surely carry 10 – 14% of the total questions. If you are lucky enough, you will get more than that. I am saying this because it is not a difficult topic. So, the more questions, the more opportunity you have to score.
The chapter on Modern Physics JEE Main is one of the highest scoring topics. It makes up about 14% of the total number of questions. Sometimes, questions are also repeated in the JEE from this topic. The numericals from this chapter are not too difficult, as the level generally lies between easy to moderate difficulty.
Some of the most important topics are Photoelectric effect, Bohr’s theory of hydrogen-like atoms, and De Broglie wavelength of matter waves. One should, however, not leave the other topics unattended as modern physics is an easy to score section and does not take much time to cover. Semiconductor Devices and Communication Systems are the chapters which are present only in the JEE Main syllabus, and one will find questions from these topics almost every year.
Students generally neglect logic gates, which is a subtopic in Semiconductor Devices. But this is an important topic from a competition point of view–as even a difference of a single mark might decide whether you get your desired branch in your desired institution.
For Semiconductor Devices and Communication Systems, one should cover NCERT books thoroughly. Be aware that even most of the institute teachers don’t take these two chapters seriously, so you must cover these chapters on your own if you’re aiming for a top rank. Sometimes, examples of NCERT have directly showed-up in the JEE Main from these chapters.
For other topics, one should read the following books
After solving these books you should go for previous years’ questions. One should solve the previous year archives for Physics and all other subjects because almost 10 – 20% of the paper will be similar to questions which have come in previous years, particularly for the JEE Main. Even if some questions are not based on previous years’ questions, at least you will get confidence because you were able to solve questions which came in the JEE before.
Now, we come to the most important subtopic of this article.
How should you study? How much time should you give to each topic? And what is the perfect method to retain Modern Physics JEE (or any related topics) in your mind?
I would suggest you make notes. Because notes are very helpful at the time of revision. You will revise the whole topic in much less time and you can carry your notes anywhere. Let us start:
Give 4 days to semiconductor devices and communication systems.
The idea is to alternately read theory and solve problems so as to maintain the right balance.
You can modify this strategy according to your comfort and convenience, but try to give sufficient time to every topic. Now, after completing the whole syllabus of Modern Physics JEE, the next thing that is important is regular revision. Let’s talk about how to revise modern physics or any other subject.
If you have followed the above strategy, it will take much less time to revise. The best strategy for revision is that you should revise every weekend. If you revise frequently, you will have no fear of tests in coaching. I would suggest you revise notes on every Sunday. This should leave you with a strong grip over what you have studied before. I suggest you follow this revision technique for every subject as it is very helpful.
In JEE preparation if you are not managing time, you are not preparing at all. Everybody has heard time management is the key to success. But, how many of us apply this to our daily lives? I guess those who apply this are successful.
You have to manage your time because you will have a lot to study in a very limited time. I would suggest you make a timetable. The timetable should include time for outdoor activities too because a healthy mind resides in a healthy body. Don’t exhaust yourself. Studies should be your first priority but give time to other things as well.
Now, that was all about Modern Physics. I have tried to cover all the topics that you should keep in your mind to excel in Modern Physics for the JEE. I would again emphasize not ignoring this topic as it is high scoring and easy.
I know JEE is one of the toughest examinations, but do not get bothered about that. Focus on yourself. If you keep focusing on the fact that the JEE is difficult, or that you have a lot of competitors–it will only negatively affect your performance. Don’t think about unnecessary things. Just focus on learning as much as you can, and you will eventually do well.
I know getting into an IIT is a beautiful thing! But it is not the only beautiful thing. Preparation for the JEE is a stressful journey but remember–it’s about the journey, not the destination. You will come to learn many things in this beautiful journey.
All the best for future!
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]]>To ensure that your efforts produce the desired result, you must know where to channel your efforts.
Of the three subjects tested by the JEE, Physics is a really important subject. If mastered well, knowing Physics can definitely lead to great results.
So, in this article, we will discuss the topics in physics that are highest scoring.
The first topic is BASIC UNITS AND MEASUREMENTS.
This topic is the most basic of all topics. This part basically tests our familiarity with the measurement instruments of various scales. If you make sure to clear all of the basic concepts and formulae regarding this topic, then this part can really help you score a lot of points! Questions from this topic definitely find substantial portion in JEE MAINS and also in ADVANCED.
The next important topic we’ll talk about is MECHANICS. I am sure that mechanics is a nightmare for beginners, but with the progression of time you might start loving it! There is much diversity within this topic: ranging from kinematics to rotational motion. Starting with kinematics, you must have a clear understanding of vectors and basic math–as this will prepare you well to solve questions in kinematics.
The next important topic is NEWTON’S LAWS OF MOTION. This is one of the most high scoring of the JEE important topics within Physics. You definitely need to thoroughly understand the concepts of friction, pulleys, strings, springs, circular motion, inclined planes, and so on.
One somewhat easy topic from mechanics is WORK, ENERGY, and POWER. There is not much of a variety of questions that are asked from this section. But keep in mind that CONSERVATION OF ENERGY is important, and GRAVITATION is an easy to score topic.
The next of the JEE important topics is ROTATION. Some
really mind-boggling questions are asked on this topic. Because a good number of questions are asked from this chapter, you should be sure to practice as many of these questions as possible, and become fluent in the topic. Learning rotation well requires really dedicated effort, but once you master the concepts it can be very high scoring and a great rank booster.Other topics in mechanics include Centre of Mass, Momentum Conservation, and Simple Harmonic Motion. Out of these, SIMPLE HARMONIC MOTION is the most important as this will lay the foundation for some subsequent chapters. These topics must be practiced a lot to improve your overall score.
Well, you might be thinking that I listed almost every topic from mechanics, but trust me, MECHANICS is an extremely important topic from which many questions are asked.
The next topic is FLUID DYNAMICS AND ELASTICITY. Questions from fluid dynamics are relatively easy. This makes fluid dynamics a really great area where you can pick up a lot of points. Continuity equation, Bernoulli Equation, Variation of pressure with depth, surface tension, stress-strain curve, and a plethora of equations are the most significant constituents of Fluid Dynamics and Elasticity. So try to practice as many questions as possible to ace your performance.
The next scoring section is HEAT AND THERMODYNAMICS. It is a major topic from which easy questions are asked. Questions from Calorimetry, Laws of Thermodynamics, Kinetic Theory of Gases frequently appear on the exam.
And just because the questions are relatively easy, this is not a reason to short-circuit your studying of this topic. You really need to understand the concepts very well to be able to understand the questions asked, and pick up all those extra points.
Generally, questions on thermodynamics have many steps and are based on inter-related concepts. So it is really essential to manage your time well when answering these questions, and have a clear understanding of the concepts involved. Mastering this topic will also benefit you in Chemistry as it is a common topic, the only thing you need to be careful about is the sign convention.
Moving forward, the next extremely important section is ELECTROMAGNETISM. It is an uphill task to score decently without having a deep understanding in Electromagnetism. This topic is quite difficult and diverse as well. But you must know that “difficult” is a relative term. Your dedication and love for the topic can make it easy for you. Topics like Coulomb’s law, Gauss law, Potentials, and Capacitors require practice.
After Electrostatics comes Current Electricity. Electrostatics and current electricity have a lot of formulae and derivations. Never decide to skip derivations, they are extremely important for concept build-up. Also, remember that current electricity is a really easy topic to score on if studied well.
Next topic is MAGNETISM. It is a topic which requires greater efforts but it is high scoring. This topic also has lots of formulae and derivations. But here, the derivations are extremely important. These derivations can frequently be the basis of many questions. Ampere’s Law is important.
In this topic, direction plays a crucial role. Be careful that you never mess up with the directions–because sometimes these mistakes can result in a great loss of marks.
These were comparatively difficult topics. There are easy topics as well which have a significant percentage and easy scoring too like Oscillations and Sound, Modern Physics being the most scoring of them. The questions from these topics are not very difficult or time-consuming. Also, these topics are really easy to comprehend. But still, never stop practicing as ”Practice makes a human perfect”. For such topics try to make your speed a plus point.
Try questions from archives as they let you know what is expected of you. I suggest that you should never be solely dependent on these archives. You must be conceptually strengthened to face any sort of questions asked. The JEE is well known for the mind-boggling questions which require on the spot thinking. They can ask questions on a totally unexpected situation using some really simple concepts.
So these were the JEE important topics that will get you the most points in Physics. Make sure to practice a variety of questions and even try to attempt a question in multiple ways. This will eventually lead you to find out alternate ways to reach the answer quickly. Focus more on concepts, but at the same time do not forget to learn the formulae. Be regular in your practice and sole as many mock tests as possible.
Lastly, I will say that throughout your preparation journey, there will be instances when you may feel that it is getting really difficult to continue, and you may even want to quit. At that time, you must remember, ”Success comes to those who wait” and “Failures are the stepping stones to success”. The path you have undertaken is not easy, there will be moments of failure, but it is up to you to decide whether to quit or to work even harder to reach your ultimate goal.
“WINNERS NEVER QUIT AND QUITTERS NEVER WIN”
Best of luck and have an enriching journey ahead!!!
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]]>The post Calculus Made Easy for JEE Physics appeared first on Magoosh JEE Blog.
]]>Physics is all about occurrence, observation, logical comprehension, and prediction. It primarily is a unique blend of the phenomenon of numerous incidents, a plethora of unknown activities, and an altogether amalgamation of what humanity has been observing throughout history. And you should always try to be aware of the fact that Physics is the gateway which leads us through the ignorant inner-self to the actual happenings around the world.
The Joint Entrance Examination (or JEE) for admissions into the top-notch colleges of the nation, needs its candidates to be the best at comprehending these ongoing occurrences, and coming up with the best innovations the world has ever witnessed.
Being a JEE aspirant, you must have heard of the close link between Physics and Mathematics, either through your high school Mathematics teacher, or any peer who scores well at Mathematics. It’s often seen that the students not opting for Mathematics tend to have a not-so-good view of the Physics in their curriculum—and they avoid being wholly engrossed in the concepts of Physics.
“THE WORLD IS CHANGING.” This proverb is one of the best that can be used to describe Physics and its connection with the world. By this proverb, we don’t only mean any single entity. It signifies every entity which is a constituent of the world, however small it may be. You can’t ignore the little termite which can change the layout of the furniture, nor can you overlook the increasing effect of pollution on the rise in average temperature over the years. In totality, to study the environment, the sequences, and the occurrences, you must find and focus on the smallest entities you can discover.
Physics is a subject where you find entities which are changing with time, space, and the environment. Nothing is constant in Physics, and everything is bound to change. Thus, the phrase “The World Is Changing” sums up the requirement of Calculus and hence, Mathematics in Physics.
You must have observed the common phenomenon of cooling of a substance under ambient conditions. How often do our mothers put a hot pan of water into cold surroundings to cool itself? No doubt, the rate at which the cooling process occurs depends on the surroundings. More often, we switch on the fans to allow for better cooling to take place. The common observation is how the rate of cooling depends on the surroundings, the rate of change of temperature of the vessel, and the passage of time. Thus, there are many of these variable parameters and so many of them are changing!
Calculus, allows us to study the characteristics of this changing world. Physics and Mathematics (in the form of Calculus) answer all the phenomena of the universe. To your amazement, even the most important, and the so-called mathematical derivations, have been proposed by some of the most exceptional physicians in the history of humanity. But you should not ponder over the complex calculus equations, derivations, and formulations.
Calculus in Physics is just a small part of these complex derivations. The most important concept of Calculus used in Physics is the concept of Differentiation and Integration. Both of these are used to analyze the variation of quantities over a changing parameter, be it time, distance, or any other physical parameter. Thus the Calculus in Physics is a “Calculus made easy” for the students to learn and concentrate on the actual physical phenomenon more than the mathematical derivations.
For students preparing for the JEE, it is highly recommended to learn the applied Calculus in Physics. You can learn Calculus made easy for the sole purpose of application in Physics. These include
You get to know the basic Mathematics long before it is taught in the regular Mathematics classes, as the Mathematics classes would be in much more detail.
The Calculus has been made easy by elementary knowledge of derivatives, integrations, and graphs of some of the primary functions as a part of JEE Physics. Physics deals with qualitative concepts, The integration of Calculus into current physical world situations has helped humanity discover the vast potential of Calculus, which turns the subject from a qualitative one to a qualitative and quantitative domain.
In a way, the results from Mathematics are directly used in Physics, and this has made Calculus easier than what it sounds to the human ear. So, without pondering over how you could make it through the giant equations and derivations of Calculus, you should start the Calculus-made-easy. This is the Calculus which is required to understand the concepts of this qualitative subject, Physics.
Without much ado, you should start the proceedings—just keep in mind that a mere beginning can transform you from a novice to an adept in this exciting venture.
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]]>Current, in a conductor, is defined as the rate of flow of charge across any cross-section of the conductor.
I=Q/t where
Q=charge, t=time
If flow of charge is non-uniform,
I=dq/dt
You can also find the amount of charge flown in a certain time by finding the integral of Idt.
The velocity with which the free electrons are drifted towards the positive terminal, under the action of the applied field, is called the drift velocity of the free electrons.
v = (eV/ml)\t
Here, e is the charge of the electron, V is the potential difference, m is the mass, l is the length of conductor and t is the relaxation time.
Here, you can notice that this formula can be written in many ways by manipulating the formulas of e or V. Take care of this while solving problems, try to keep it as simple as you can. By writing what is given and what is to be found, there’s no big deal solving problems related to it.
As I mentioned above, there’s also a famous relation between electric current and drift velocity.
I=nAve (you should try to derive this by your own)
According to ohm’s law,
V=IR
R=resistance
Few more basic formulas:
ρ_{t}= ρ_{0}[1+α(T-T_{0})]
since resistivity is directly proportional to resistance you can replace ρ with R in this equation.
R_{t}=R_{0}[1+α(T-T_{0})]
Here, R_{t},R_{0} is the resistance of the conductor at tº C and 0º C respectively.
Please note that this formula is valid only for the very low value of α.
Conductivity is the reciprocal of Resistivity, same for conductance and resistance.
Current density J is equal to current divided by area.
J is a vector quantity.
J=I/A
J= σ e
dW =IVdT
P= I^{2}R = V^{2}/R
dW =energy dissipated
P =power
When in series:
R_{eq} = R_{1} + R_{2} +R_{3} +…..
Solving problems related to this are very easy, I will be same in each R. You can simply apply Kirchoff’s law to get the answer.
When in parallel:
1/R_{eq} = 1/ R_{1} + 1/ R_{2} +1/ R_{3}
Here, current is divided in different branches but the Voltage across each cranch is same.
The electromotive force E of a cell is defined as the difference of potential between its terminals when there is no current in the external circuit, i.e., when the cell is in open circuit.
The potential difference of a cell is the difference of potential between two terminals when it is in closed circuit.
E = V+IR
The resistance offered by the electrolyte of the cell when the electric current passes through it is known as the internal resistance of the cell.
Internal resistance(r) , r=E/(R+r)
I = I^{2}RT Joule
Power consumed in series and parallel combination holds the same relation as of the resistance.
Total emf of the battery = E
Total Internal resistance of the battery = r / n
Total resistance of the circuit = (r / n) + R
I=nE /(nR +r)
Total emf of the battery = nE (for n no. of identical cells)
Total Internal resistance of the battery = nr
Total resistance of the circuit = nr + R
I= nE /(nr+R)
Problems are generally simple and formula based, so you won’t find any difficulty in these if you apply them properly.
In balanced condition, the galvanometer shows no deflection. The condition is:
Rx/R1 = R3/R2
The current won’t flow through G, the circuit will be equivalent to removing G in above diagram.
In balanced condition,
R/S=x/100-x
So, that was the summary of the chapter current electricity. I hope this chapter won’t bother you much but please pay good attention and practice more no. of problems. You’ll have a good time during exams.
All the best.
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Electrostatics — as the name suggests — is the study of electric charges at rest (in the realm of classical physics). But what is an electric charge? It may be hard to define charge but just to give you an idea: suppose you run a spoon through oil, and then graze it over a very small (caution here) piece of paper. You’ll notice the piece of paper getting attracted to it. This attraction is due to a phenomena of charge induction, or simply put, due to the presence of a charge on the body
Now that you understand the context, let me put up some bizarre rules. “Like charges repel each other and unlike charges attract each other.”
This statement refers to the way charges are defined. A positive charge attracts a negative or uncharged object, but repels a positively charged object, and vice versa.
It’s interesting to note that if charges attract or repel each other, there must be a governing law for the same. The answer to this problem was posted by Newton when he gave an analogy between gravitation and electrostatics (more on that later). He concluded experimentally, that two charges (points Q1 and Q2), at rest placed at a distance (R) from each other exert a force on one another. This force is proportional to the product of the magnitude of the individual charges and inversely proportional to the square of the distance between them. The constant of proportionality K has a value equal to 9*109 in SI units and 1 in CGS units. This K is dependent on the surroundings of the two charges.
Electric Field is another important parameter in the study of Electrostatics. This term gets its definition from the Force relation only. It is the force exerted by a charge on a test charge (+ve and very small magnitude) which is placed at a distance (R) from it. Electric Field calculations are quite vital in both JEE Main and Advanced. Though most problems are solvable by integration, there are some tricks and short cuts to bypass integration or at least simplify it.
One such application involves the concept of Electric Flux and the famous Gauss Law. Electric flux is defined for an electric field as the measure of number of field lines crossing a unit area per unit time. This can be considered somewhat similar to density of field lines in an electrostatic field. The Gauss Law, relates electric flux due to a charge distribution over a surface to the quantity of charge present strictly inside the surface.
The Law states that Flux passing through a closed surface is equal to the quantity of charge inside divided by permittivity of vacuum which is equal to 8.85*10-12 in SI units. The point to be noted here is that flux can also be defined as surface integral of Electric Field due to some charge distribution over a closed surface. The Gauss Law stated above simplifies the calculation of electric field to a great extent in case of symmetry elements. For example, calculations for electric field inside a solid sphere with uniform volume charge density can be easily calculated using this law. You don’t need to integrate, just use concepts of symmetry and calculate charge inside the surface by using the uniform nature of charge distribution.
Another very important concept in Electrostatics for the JEE is Interaction Energy between a system of discrete or continuous charges. However, calculating this requires the use of electric fields too, highlighting why electric fields have been a hot topic on the exam. Interaction energy can be loosely defined as the energy required to arrange the system in given conditions from infinite separation reversibly. The word reversible here refers to assembling the system in a very slow manner, ie: no acceleration for any of the charge by applying a variable force at each instant which just balances the electrostatic force.(Not doing so, changes the chapter).
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Self Energy of a system is new favorite for JEE paper setters. Self energy of a point charge is ideally not defined but if you want to give it mathematical form, it would be very high. For other charge distributions, this refers to energy of making the system.
It is necessary to understand the difference between the two energy terms.
Self energy is always positive since you have to do work to assemble the system, no charge wants by itself to leave infinite separation and come in an ordered state (Entropy Considerations, can somehow be related here).
Total energy of a pair of systems is the summation of Self Energy and Interaction Energy of the two. It is this total electrostatic energy which is conserved, the individual energies might change. So I would suggest while solving the JEE paper, be careful what to conserve and what to change.
Some good books to refer to for this very important topic would be – H.C.Verma, Electricity and Magnetism by DC Pandey.
I hope all this information helped introduce you to the various portions of electrostatics that you will surely be tested on!
Wishing you best of luck, Cheers!
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]]>Statistics have always suggested that in general, among all the three subjects, students struggle when it comes to scoring high in Physics. The average score of most of the students is lowest in Physics. Here we are, trying to list down some topics which are very important for JEE Main Physics, which will help you to prepare in a smarter way.
Broadly, we can divide JEE Physics into 5 parts:
This is the most important unit for JEE Main Physics.It covers about 25% of weightage of JEE Main Physics Paper.This unit comprises of topics like:
This unit approximately covers 13% of JEE Main Physics paper and is again very important.
We can divide this unit into 3 Major parts.
These both units covers about 10% of JEE Main Physics paper.You should know how to calculate time period of SHM for various assemblies, Phasor technique, Relation between Kinetic energy, Potential Energy.
Waves in itself is a very vast topic and have many subtopics.For JEE Main Physics, you can focus on equations of the wave in sinusoidal form, harmonics of a wave, Pressure and density variations for a wave, Doppler Effect.
These two units are very very important for JEE Main Physics.Both units cover about 17-19% of the Physics Paper, with Modern Physics being more important.
For Ray Optics you should be thorough with the concepts of Reflection, Refraction, Total Internal Reflection, Snell’s Law, Geometrical Optics.
In Wave Optics you should be well acquainted with Huygens theory, Diffraction principle, Polarisation of light, Brewster’s law.
For Modern Physics you should have a grip on concepts of Atomic structure, Bohr Model of Hydrogen atom, Threshold energy, De-Broglie explanation of the matter, Nuclear Physics, X-Rays.
This was theoretical description about all the important topics for JEE Main Physics. JEE Main Physics is more about speed,accuracy and practice. It is a strong recommendation that you should memorise the standard results, formulae of each topic. This is a must to score good in physics.
Lastly you should also practice previous years’ question papers. They are very important.
All the best!
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]]>The type of questions which are being asked in JEE nowadays definitely use the concept of magnetic lines of force. Sometimes, questions are framed on the properties of field lines, especially in JEE Mains. You must go through a standard book such as NCERT and H C Verma for reading, understanding the concepts and problem-solving.
Find the magnitude of force per unit length exerted by two thin long parallel wires separated by a distance ‘b’ and carrying a current ‘i’ ampere each. (Previous Year IIT-JEE Question)
Force per unit length acting between two wires carrying currents i1 and i2 at a separation distance r is given by
F/L = µ_{0} (i_{1}*i_{2})/2πr
Here, i_{1} = i_{2} = i and r = b
Thus, F/L = µ_{0} (i*i)/2πb
Hence, from the above discussion, we conclude that option (2) is correct.
The Magnetic lines of force inside a bar magnet (Previous Year JEE Main Question)
Clearly the correct answer is option (1).
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]]>JEE Mains Physics syllabus contains some chapters that are difficult, and some that are easy. Among these chapters, Electricity and Magnetism is one of the toughest in terms of understanding the concepts behind each topic, and the difficulty level in numerical problems. But if you have a strong hold over these chapters, you can easily be assured of 25% of JEE Mains Physics. But remember things may get a bit tricky if ‘taken for granted’.
The kind of questions that are asked in the JEE Mains from Electricity and Magnetism are very much practical and application-based. Hence, they are easily understandable as the learners can relate it to their daily life experiences. It is very important to visualize the given question while trying to figure out the solution. ‘Electricity and Magnetism’ contributes about 5 – 6 questions in JEE Mains. If you skip these chapters, you are going to be at a great loss.
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