Magnetic Flux In a Coil: 7 Important Facts You Should Know

by

In this article we are going to describe 7 important facts related to magnetic flux in a coil.

Magnetic flux in a coil is basically the total number of magnetic field lines that are passing through a total surface area of the coil. As we know magnetic field lines are basically the measure of net magnetic field of a surface hence it is clear that the net magnetic field that is passing through that given surface area is known as magnetic flux of that surface.

Here we  need to clarify one thing that there is a difference between the total number of magnetic field lines and the net number of magnetic field lines. The net number of magnetic field lines means the difference between the number of magnetic field lines that are directed in one direction and the number of magnetic field lines that are directed in another direction.

The general expression of magnetic flux is- Φ = B.A = BAcosθ where B is the magnetic field and A is the area and θ is the angle between B and normal of the plane. There are two types of magnetic flux. One is magnetic flux through a closed surface and another is magnetic flux through an open surface. Magnetic flux through a closed surface is always zero but magnetic flux through an open surface is not zero.

How magnetic flux is produced in a coil?

The reason behind the generation of magnetic flux in a coil is electric current. Now we will describe how magnetic flux is produced in a coil with the flow of current and also we will give a clear picture of how magnetic flux that is linked to a coil changes.

Let’s take an example of a current carrying coil and a magnet that is placed in front of it. When this magnet is brought closer to the coil or far from the coil there will occur an effect in the coil. That effect is known as magnetic flux. Actually the movement of a magnet brings changes in the magnetic field of the coil. In this way magnetic flux is produced in it.

This phenomenon of inducing magnetic flux in a coil by bringing a magnet closer or far from the coil is known as the principle of induction. With the help of this principle magnetic field or more specifically magnetic flux can be induced using a magnet.

How to calculate magnetic flux linked with a coil?

Now we will calculate the value of magnetic flux that is linked with a coil. Say there are N number of turns on the given coil and the cross sectional area of it is A. The plane of the coil is kept parallel with respect to the magnetic field. So the mathematical expression for calculating the magnetic flux linked with a coil is  Φ = Nx(B.A) = NBAcosθ

WhereN is the number of turns around the coil,B is the magneticfield andA is the area and θ is the angle betweenB andnormal of the plane. Here the angle between the magnetic field B and the normal of the plane is 90 degrees. It means that θ = 90 degrees. Therefore , Φ = NBAcosθ = NBAcos90 = NBAx0 = 0 [ as cos 90=0]. So the value of magnetic flux linked with a coil is zero when its plane is parallel to the magnetic field.

How does magnetic flux change through a coil?

Magnetic flux linked with a coil changes according to Faraday’s laws of electromagnetic induction. First law states that the change in number of net magnetic field lines or more specifically the magnetic flux linked with the coil induces an emf or voltage in the coil.

Second law states that the rate of change of magnetic flux is equal to the induced emf that has been generated within the coil.

The required mathematical expression for the second law is-

∈ ∝ – dΦ/dt where ∈ is the induced emf. Now if there are N number of turns in the given coil then this expression will be written as ∈ = – N.dΦ/dt. This (-) sign signifies that the induced emf tries to defy the change in magnetic flux.

As Φ can also be written as Φ = ∬ B.dA (where dA is the value of infinitesimal area),the above expression of induced emf can also be written as ∈ = – N.d/dt(∬ B.dA). Using three methods we will be able to change the value of the magnetic flux linked with the coil.

  1. If we change the strength of the magnet – if the strength of the magnet is increased it means that the value of the magnetic field will also be increased. Due to the increased magnetic field induced emf will also increase as it is directly proportional to the magnetic field.
  2. If we change the surface area- as the induced emf is directly proportional to the surface area hence induced emf will increase with the increasing value of surface area and induced emf will decrease with the decreasing value of surface area.

 3. Any change that is occurred in the angle between the magnetic field and the normal to the plane is also another reason of change of the value of induced emf.

When a wire loop is rotated in a magnetic field?

With the help of a very simple example we will be able to answer this question. Let us take the value of magnetic flux as a function of frequency w of the moving coil. Φ = BAcoswt

Therefore ,  ∈ = – dΦ/dt = -d/dt(BAcoswt) = wBAsinwt

When the value of wt is in between 0 to π then the value of sin wt is +ve whereas the value of sin wt is -ve when the value of wt lies between  π and 2π. The magnetic flux is used to pass through the coil when the coil starts rotating at the position where its plane is normal to the magnetic field.

As the coil starts to rotate the magnetic flux that is linked with the coil gets lower value. In this way when its plane becomes parallel to the magnetic field then the value of the magnetic flux becomes zero. After that the value of flux again starts increasing. If the coil keeps rotating then again the value of magnetic flux will reach the maximum value.

What are the three factors which cause a change in magnetic flux of the coil?

The three factors that cause a change in the magnetic flux of the given coil are- (1) magnetic field (2) surface area and (3) angle between the magnetic field and the normal to the plane.

1.If we change the strength of the magnet – if the strength of the magnet is increased it means that the value of the magnetic field will also be increased. As induced emf is directly proportional to the magnetic field hence induced emf will also increase.

2.If we change the surface area- as the induced emf is directly proportional to the surface area hence induced emf will increase with the increasing value of surface area and induced emf will decrease with the decreasing value of surface area.

3.Any change that is occurred in the angle between the magnetic field and the normal to the plane is also another reason of change of the value of induced emf.

Practice Problem

A uniform magnetic field of 0.2 T makes a circular loop to rotate. The area of the circular loop is 1×10-2 m2. If the plane of the loop is perpendicularly kept with respect to the magnetic field then calculate the value of magnetic flux.

Answer :

B= 0.2 T

A= 10 x 10-2 m2

θ = 0 degree

We know, Φ = BAcosθ

                          = 0.2 x 10 x 10-2 x cos 0

                          = 2 x 10-2 weber

Conclusion

In this article we have discussed several facts that are related to magnetic flux in a coil.

Also Read: