First slide

Motional EMF

Question

The spokes of a wheel are metallic and their length is 0.5 m. On rotating the wheel at right angles to a uniform magnetic field of 5 x 10^-4 tesla, a potential difference of 3.14 mV is produced between the rim and the axis. The rotational speed of the wheel is

Easy

A

8 rotations/sec
B

12 rotations/sec
C

16 rotations/sec
D

20 rotations/sec

Solution

We know that, $e = \frac{1}{2} {Bl}^{2} ω$
$Here ω = 2 πn$
$\begin{array}{l} ∴ e = \frac{1}{2} {Bl}^{2} (2 πn) or n = e / ({Bl}^{2} π) \\ or n = \frac{3 \cdot 14 \times 10^{- 3}}{(5 \times 10^{- 4}) (0 \cdot 5) (3 \cdot 14)} = 8 rotations/sec \end{array}$

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