First slide

Magnetic flux and induced emf

Question

A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicularly to the plane of the coil. The radius of the coil changes as shown in figure.
The graph of magnitude of induced emf in the coil is represented by

Moderate

A
B
C
D

Solution

In the r-t graph, it is clear that from a to b there is no change in radius and hence no change in area and magnetic flux. Same is the situation from c to d.
$\begin{aligned} \begin{array}{l} Now, | ε | = \frac{d}{d t} (ϕ) \\ F o r b t o c, \\ \Rightarrow | ε | = B \frac{d}{d t} (π r^{2}) = B π 2 r \frac{d r}{d t} \\ Since r \propto t, \\ ∴ \frac{d r}{d t} = constant \\ ∴ | ε | \propto r \end{array} \end{aligned}$

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