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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 ϕ−t graph gives us the induced e.m.f

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