First slide

Magnetic flux and induced emf

Question

A conducting ring of radius r is rolling without slipping with a constant angular velocity $ω$ (figure). If the magnetic field strength is B and is directed into the page then the emf induced across PQ is

Moderate

A

$B ω r^{2}$
B

$\frac{B ω r^{2}}{2}$
C

$4 B ω r^{2}$
D

$\frac{π^{2} r^{2} B ω}{8}$

Solution

Join PQ with an imaginary line which is instantaneously rotating with $ω$ about point Q.
$\begin{array}{l} | E | = Magnitude of induced emf \\ \begin{array}{c} = \frac{B ℓ^{2}}{2} ω \\ h e r e ℓ = \sqrt{2} r \\ \Rightarrow E = \frac{B (2 r^{2}) ω}{2} = B ω r^{2} \end{array} \end{array}$

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