# JEE Topics: Magnetic Lines of Force

To describe phenomena of magnetism, magnetic lines are used to represent the force which exists in the surrounding area. These lines are imaginary and do not exist practically. Magnetic field lines of force can also be visualized as streamlines in fluid flow. These lines are used to represent and describe the pattern of the field. Tangent at any point on the line will give the direction of magnetic field at that point. Field lines are just an aid for visualization, like ‘lines of current in a river’, the water is flowing everywhere but the direction of flow is a bit different at each point.

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.

## Basic Key Points about Magnetic Lines of Force

• Magnetic field lines depict a path which points in the direction of the field at every point along it. These lines do not have any origin or end, and also, do not intersect at any point in space because if they intersect then there would be two directions of magnetic field at a single point which is not possible.
• Another advantage of using field lines as a representation of intensity and force is that many laws of electromagnetism can be stated completely using only the simple concept of ‘number of field lines’ through a surface.
• Magnetic field lines can be displayed by several physical phenomena. For example, when iron filings are placed in a magnetic field it forms certain curvature corresponding to the field lines. Field lines are thus, used as a ‘qualitative tool’ to visualize magnetic forces.
• In a Bar Magnet, Magnetic lines are assumed to originate from ‘North Pole’, and then arrive at the ‘South Pole’ while traveling in the surrounding space. But inside the magnet, these lines move from the South Pole to the North Pole and hence complete the loop.
• At the poles of any magnet, the magnetic field is the strongest because lines of force are crowded together at that place. As we move away from the poles, strength of magnetic field decreases continuously. Direct conclusion which arrives from the above fact is that Magnetic field intensity depends on the “number of lines of force”.
• The number of magnetic lines of force passing through a normal unit area is known as magnetic induction, whereas the number of magnetic lines of force passing through a given area is known as ‘magnetic flux’.

## Properties of Magnetic Lines of Force

• The number of lines of force per unit area (when the area is taken perpendicular to the lines) is proportional to the strength of the field at that point. So, more concentration of lines would represent a stronger magnetic field.
• Magnetic lines of force tend to contract lengthwise that is they possess longitudinal strain, due to which two unlike magnetic poles attract each other.
• The lines of force tend to exert sideways (lateral) force, i.e. they repel each other laterally. This phenomenon explains the repulsion between two similar poles.
• Number of lines of force that start from a unit magnetic pole is equal to 4π. The ‘degree of closeness’ of the lines of force shows the relative strength of magnetic field at a particular point.
• Magnetic field lines may cross one another but whenever they do so, field strength has to be zero at that point. If you take a magnetic compass along the magnetic field lines, you will notice that the needle always points in the direction you are heading in, in order to stay in that magnetic field.
• The direction of lines of force at any point in space gives the direction of the ‘magnetic force’ on a ‘north pole’ placed at that point.

## Basic Experiment to visualize Magnetic lines of force

• Put a flat bar magnet down on a plain sheet of paper or cardboard. Take a small magnetic compass which points in the north direction when left free.
• Now, take the magnetic compass and keep it on the sheet of paper in the vicinity of the bar magnet.
• The direction where the magnetic compass points will tell you the presence of the bar magnet and show the direction of the field, at the location of the magnetic compass.
• Do this at different points on the paper, and you will be able to trace the magnetic field lines. The field lines are surely imaginary but can be visualized in this way for proper understanding.

## Some JEE Problems

### Question:

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)

1. µ0 (i*i)/b*b
2. µ0 (i*i)/2πb
3. µ0i/2πb
4. µ0i/2πb*b

#### Solution:

Force per unit length acting between two wires carrying currents i1 and i2 at a separation distance r is given by
F/L = µ0 (i1*i2)/2πr
Here, i1 = i2 = i and r = b
Thus, F/L = µ0 (i*i)/2πb
Hence, from the above discussion, we conclude that option (2) is correct.

### Question:

The Magnetic lines of force inside a bar magnet (Previous Year JEE Main Question)

1. are from south pole to north pole of the magnet.
2. are from north pole to south pole of the magnet.
3. do not exist.
4. depend upon the area of the cross-section of the bar magnet.

#### Solution:

Clearly the correct answer is option (1). 