Magnetic Flux And Magnetic Induction: 7 Important Facts

In this article we are going to discuss 7 important facts that are related to magnetic flux and magnetic induction.

If any change occurs in the value of magnetic field that is linked with a current carrying conductor there will be production of induced electromotive force. This phenomenon can be referred to as electromagnetic induction. Once a magnet is brought closer to a current carrying wire there will be change in magnetic field as well as magnetic flux within the conductor. This incident is known as magnetic induction.

Hence it can be said that both magnetic flux and magnetic induction are related to each other. It can also be concluded that due to magnetic induction there occurs a change in the magnetic flux linked with the current carrying wire. So magnetic induction is the cause and magnetic flux is its effect.

Now we will try to give a clear idea of magnetic flux. Basically the net number of magnetic field lines that are passing through a definite area is known as magnetic flux. It has been cleared from the above lines that magnetic flux and magnetic induction are two different quantities. Magnetic flux is a scalar quantity whose SI unit is weber whereas magnetic induction is a vector quantity. Magnetic induction is basically equivalent to magnetic field. Magnetic flux  Φ= B.A=BAcosθ (B is the magnetic induction and A is the area)

How is magnetic flux related to magnetic induction?

Magnetic induction is basically a vector quantity which has a unit of weber/m². So, magnetic field linked with a coil = magnetic induction of that coil.

 Hence through this formula it can be said that magnetic flux is proportional to magnetic induction when the area is kept constant.

Therefore , increase in the magnetic induction ∝ increase in the magnetic flux. Now if we try to go into the deep mechanism it will be seen that there is induction. So what is induction? Induction means to produce some magnetic effects in a current carrying coil by bringing a magnet closer or far from the coil but without touching. These effects that are produced within the coil are changes of magnetic field as well as magnetic flux. Hence all these three are interconnected.

There are two laws that are related to magnetic flux and magnetic induction. They are- Faraday’s laws of electromagnetic induction and Lenz’s law.

Faraday’s laws of electromagnetic induction

First law states that an emf is induced in a current carrying circular loop  when it is placed in a magnetic field that varies with time.

Second law states that the induced emf is proportional to the rate of change of magnetic flux linked with the circular loop. The value of induced emf ℰ is equal the product of number of turns(N) in that loop and rate of change of magnetic flux.

Mathematical expression for the second law is  ℰ=-N.dΦ/dt this negative sign signifies that the direction of induced emf and rate of change of magnetic flux are opposite to each other.

Lenz’s law

It states that the induced emf tries to oppose its cause. As we know that the cause of induced emf is change in magnetic flux,it means that the induced emf tries to stop the change that occurs in magnetic flux.

Differences between magnetic flux and magnetic induction

The basic difference between magnetic flux and magnetic induction i.e, magnetic field is – magnetic flux is used to measure the strength of magnetic field lines that are passing through a given definite area whereas magnetic induction or magnetic field is a region around a magnet where if some moving charges are being kept they will experience a force named as Lorentz force.

There is also another difference between magnetic flux and magnetic induction. That is – the value of magnetic flux is dependent on area as well as the strength of the magnetic field of a given magnet. But the value of magnetic induction only depends upon the strength of a given magnet.

Difference in terms of units of magnetic flux and magnetic induction:

There is a difference related to the mathematical formula. The mathematical formula for magnetic flux is Φ= B.A=BAcosθand for magnetic induction is F=qvB(this F islorentz force and q is charge and v is the velocity with which the charge q is moving in the magnetic field B).

Similarities between magnetic flux and magnetic induction

Magnetic flux and magnetic induction are two different quantities. But there is a common thing between them or it must be said that they are interrelated to each other. If we divide magnetic flux by cross sectional area or take the value of magnetic flux per unit area then that value will be equal to magnetic induction. This also has another name of magnetic flux density.

The units of magnetic flux density and magnetic induction are the same. The SI unit is wb/m².

Is magnetic flux density and magnetic induction same?

Yes both the magnetic flux density and magnetic induction are the same.

As we know, the mathematical formula for magnetic flux is Φ= B.A=BAcosθ where θ is the angle between magnetic field B and area A. when the direction of B and A are parallel to each other then θ will be zero.

Then Φ= BA as we have said that magnetic flux density or magnetic induction is number of magnetic field lines per unit area,hence magnetic flux density or magnetic induction B=Φ/A. Therefore the unit of magnetic flux density of magnetic induction in SI unit is weber/m².

What are the units of magnetic flux and magnetic induction?

I have said before that magnetic induction is a physical phenomenon but it is equivalent to  magnetic field. Hence

 The SI unit of magnetic induction is Tesla and the CGS unit of magnetic induction is Gauss.

The SI unit of magnetic flux is Weber and the CGS unit of magnetic flux is Maxwell.

Practice Problem

An electron is moving in a circular region at a velocity of 2 x 10⁸ m/s. If the force acting on the electron is 10^-4 N,what will be the value of magnetic flux if magnetic induction and area vector are parallel to each other? The area of the region is 10^-2 m².

Answer :

Charge of the electron=e=q=1.6 x 10^-19 C

Velocity = v = 2 x 10⁸ m/s

Force = F = 10^-4 N

θ = 0 degree

We know that,

F = qvB

B = F/qv

B = 10^-4/(1.6 x 10^-19 x 2 x 10⁸) T

B = 3.125 x 10⁶ T

Magnetic flux = BAcos0

                              = 3.125 x 10⁶ x 10^-2 x 1 weber

                              = 3.125 x 10⁴ weber

Conclusion

This article will be a helpful one for those who want to clear the basic idea of magnetic flux and magnetic induction. All the basics related to magnetic flux and magnetic induction have been discussed in simple words in it.

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