Electromagnetic Induction

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Common Misconceptions

6 min read

- What you are getting from a statement might not be necessarily true. Let's burst some of the common misconceptions

Does induced EMF depend on the material (resistance) of the conducting loop?
As we can see, the induced EMF does not depend on the resistance of the coil or wire.

It only depends upon the rate of change of flux which can be varied by: changing any one or more of the terms B, A and

θ

.
However, if the induced EMF produces a current, then that produced current will depend inversely on the resistance of the coil or wire (Ohm's Law). The produced current will result in a tendency to oppose the induced EMF, thereby in a tendency to oppose the rate of change of the flux (Lenz's Law).

In a loop moving in a uniform magnetic field, when the loop remains in the field, does it mean no emf is induced in it?
No, the phenomenon of electromagnetic magnetic induction still takes place in the two arms of the loop whose length is perpendicular to the direction of the velocity. However induced EMF in these 2 arms adds up and the resultant is zero since the polarity of these EMFs is opposite and equal in magnitude.

Is current induced in an OPEN conducting loop too when magnetic flux through it varies with time?
No, current is not induced in an open conducting loop when magnetic flux through it varies with time. However, EMF is induced across the open ends of the loop but the current flow is possible only when there is a closed continuous path for the free charge carriers to flow.

Is motional EMF always given by the expression "Blv"?
No, this expression is valid only when all the three quantities: B, l and v are mutually perpendicular.
The vector formula for induced EMF is:

If they are not mutually perpendicular, then we must resolve them into components and take only those components which are mutually perpendicular.
For

(v \times B)

we first take v and B $⊥$

Or we take v $⊥$ and B

Let us consider

(v \times B) = a

And then we take the projection of

a

along length

l

or since versa.

An EMF is induced across the rim and the centre of a conducting disc rotating in a plane perpendicular to the uniform magnetic field B. We see that flux through the disc is not changing and yet EMF is induced. Is it a violation of Faraday's Law?

No, this is not a violation of Faraday's Law. This paradox arises from an incorrect choice of surface over which to calculate the flux.
This won't seem like a paradox if we consider the lines of flux viewpoint: in Faraday's model of electromagnetic induction, a magnetic field consists of imaginary lines of magnetic field, similar to the lines that appear when iron filings are sprinkled on paper and held near a magnet. The EMF induced is proportional to the rate of cutting lines of flux. If the lines of flux are imagined to originate in the magnet, then they would be stationary in the frame of the magnet, and rotating the disc relative to the magnet, whether by rotating the magnet or the disc, should produce an EMF.
However, rotating both of them together should not produce an EMF as there won't be any cutting of lines of flux.

Are the formula for series and parallel combination of inductors exact?
The equivalent coefficient of self-inductance of inductors with self-inductance

L_{1}

L_{2}

...

L_{n}

in series is given by:

L_{e q} = L_{1} + L_{2} + . . . + L_{n}

The equivalent coefficient of self-inductance of inductors with self-inductance

L_{1}

L_{2}

...

L_{n}

in parallel is given by:

\frac{1}{L _{e q}} = \frac{1}{L _{1}} + \frac{1}{L _{2}} + . . . + \frac{1}{L _{n}}

However, the very important assumption while deriving these formulae is that the mutual inductance is neglected. But practically, two or more inductors in close vicinity always cause mutual induction.
The direction of flux linkage also affects the resultant self-inductance
When they have flux linkage in the same sense and

M

is the coefficient of mutual inductance between the two coils, then

L = L_{1} + L_{2} + 2 M

When they have flux linkage in opposite direction, then

L = L_{1} + L_{2} - 2 M