Question

A square loop of wire 10cm on a side with 100 turns of wire rotates in a magnetic field, |B| = 0.01T, twenty times each second. At t = 0, the normal of the loop aligns with the magnetic field. Write a symbolic expression for the voltage as a function of time starting from Faraday’s Law. Define each symbol in your expression and give its numerical value. Calculate the peak output voltage of the generator.

Answer 1

Answer with Explanation:

We are given that

Side, l=10 cm=
`10* 10^(-2) m`

1 m=100 cm

Magnetic field,B=0.01 T

Number of turns ,N=100

`\omega=20rev/s=20* 2\pi=40\pi rad/s`

Magnetic flux,
`\phi=NBAcos\omega t=NBAcos\omega t`

By Faraday's law

`V=\mid- (d\phi)/(dt)\mid =\omega NBAsin\omega t=\omega NBA sin\omega t`

Where
`\omega`=Angular frequency

N=Number of turns

B=Magnitude of magnetic field

A=Cross section area of wire

For peak voltage

`\omega t=(\pi)/(2)`

`V_(max)=NBA\omega sin(\pi)/(2)=NBA\omega=100* 0.01*(10* 10^(-2))^2* 40\pi`=

`V_(max)=1.26 V`