First slide

Motional EMF

Question

A circular coil of n t urns and radius r is placed in a uniform magnetic field B. Initially the plane of the coil is perpendicular to the field. The coil is rotated through 90^o. The resistance of the coil is ONE OHM. The quantity of charge passing through the coil is

Moderate

A

n $π$ r² B
B

n² $π$ r² B
C

n $π$ r B
D

n $π$ r B²

Solution

Rate of change of flux
$= \frac{0 - {nπr}^{2} B}{Δt} = - \frac{{nπr}^{2} B}{Δt}$
lnduced e.m.f. $= - \frac{{nπr}^{2} B}{Δt}$
$\begin{array}{l} ∴ Q = \int idt \\ = [\frac{{nπr}^{2} B}{Δt} \times \frac{1}{R}] Δt = {nπr}^{2} B \end{array}$

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