First slide

Magnetic flux and induced emf

Question

In a region of uniform magnetic induction B=10^-2 tesla, a circular coil of radius 30 cm and resistance $π^{2}$ ohm is rotated about an axis which is perpendicular to the direction of B and which forms a diameter of the coil. If the coil rotates at 200 rpm the amplitude of the alternating current induced in the coil is

Moderate

A

4 $π^{2}$ mA
B

30 mA
C

6 mA
D

200 mA

Solution

Amplitude of the current
$\begin{array}{l} i_{0} = \frac{e_{0}}{R} = \frac{ωNBA}{R} = \frac{2 πvNB ({πr}^{2})}{R} \\ i_{0} = \frac{2 π \times 200 \times 1 \times 10^{- 2} \times π (0 .3)^{2}}{π^{2} \times 60} = 6 \times 10^{- 3} A = 6 mA \end{array}$

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