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Question

Magnetic flux (ϕ) linked through the coil changes with respect to time (t) according to following graph, then induced emf (e) v/s time(t) graph for coil is:


A
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B
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C
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D
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Solution

The correct option is D
For the magnetic flux (ϕ) vs time (t) graph, the slope of the graph is equal to dϕdt.

We know that the emf induced in a coil is given by,

E=Ndϕdt

For the portion OA:

The magnetic flux increases with time at a constant rate.

dϕdt>0

So, the induced emf will be negative and is constant with time i.e. e=ve.

For portion AB:

dϕdt=0 as the magnetic flux is
Constant.

So, the induced emf will be zero i.e. e=0

For portion BC:

The magnetic flux decreases with time at constant rate.

dϕdt<0

So, the induced emf is positive and is constant with time i.e. e=+ve

Combining all the three results, the graph depicting the variation of the induced emf with time is shown below:




Hence, option (C) is the correct answer.
Why this question?
Note: According to Faraday's law,

|E|=Ndϕdt

N times the slope of ϕt graph gives us the induced e.m.f

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