Question

If I wanted to generate a maximum emf of 20 V, what angular velocity (radians/sec, aka Hz) would be required given a circular coil of wire with diameter 40 cm and 500 coils? The coil rotates through a magnet field of magnitude 9e-3 T which is directed such that the angle between the area vector and the magnet field vector varies from 0 to 2 π radians. Group of answer choices

Answer 1

Answer:

35.36776 Hz

Explanation:

B = Magnetic field = $9\times 10^{-3}}\ T$

$E_m$ = Maximum voltage = 20 V

d = Diameter of coil = 40 cm = 0.4 m

A = Area = $\pi \frac{d}{2}^2=\pi 0.2^2$

N = Number of turns = 500

$\omega$ = Angular velocity

Maximum emf is given by

$E_m=NAB\omega\\\Rightarrow \omega=\frac{E_m}{NAB}\\\Rightarrow \omega=\frac{20}{500\times \pi\times 0.2^2\times 9\times 10^{-3}}\\\Rightarrow \omega=35.36776\ Hz$

The angular velocity would be 35.36776 Hz