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

35.36776 Hz

Step-by-step explanation:

B = Magnetic field =
`9* 10^(-3)}\ T`

`E_m` = Maximum voltage = 20 V

d = Diameter of coil = 40 cm = 0.4 m

A = Area =
`\pi (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=(E_m)/(NAB)\\\Rightarrow \omega=(20)/(500* \pi* 0.2^2* 9* 10^(-3))\\\Rightarrow \omega=35.36776\ Hz`

The angular velocity would be 35.36776 Hz