Question

A 0.45 m radius, 500 turn coil is rotated one-fourth of a revolution in 4.01 ms, originally having its plane perpendicular to a uniform magnetic field. Find the magnetic field strength in T needed to induce an average emf of 10,000 V.

Answer 1

B = 0.126 T

Step-by-step explanation:

As per Faraday's law we know that rate of change in magnetic flux will induce EMF in the coil

So here we can say that EMF induced in the coil is given as

`EMF = (\phi_2 - \phi_1)/(\Delta t)`

initially the coil area is perpendicular to the magnetic field

and after one fourth rotation of coil the area vector of coil will be turned by 90 degree

so we can say

`\phi_1 = NBAcos 0 = BA`

`\phi_2 = NBAcos 90 = 0`

now we will have

`EMF = (NBA)/(t)`

`10,000 V = ((500)(B)(\pi * 0.45^2))/(4.01* 10^(-3))`

`B = 0.126 T`