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.

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lublana lublana · Answer 1 · 2020-04-10T08:18:16+02:00

Answer with Explanation:

We are given that

Side, l=10 cm=[tex]10\times 10^{-2} m[/tex]

1 m=100 cm

Magnetic field,B=0.01 T

Number of turns ,N=100

[tex]\omega=20rev/s=20\times 2\pi=40\pi rad/s[/tex]

Magnetic flux,[tex]\phi=NBAcos\omega t=NBAcos\omega t[/tex]

By Faraday's law

[tex]V=\mid- \frac{d\phi}{dt}\mid =\omega NBAsin\omega t=\omega NBA sin\omega t[/tex]

Where [tex]\omega[/tex]=Angular frequency

N=Number of turns

B=Magnitude of magnetic field

A=Cross section area of wire

For peak voltage

[tex]\omega t=\frac{\pi}{2}[/tex]

[tex]V_{max}=NBA\omega sin\frac{\pi}{2}=NBA\omega=100\times 0.01\times(10\times 10^{-2})^2\times 40\pi[/tex]=

[tex]V_{max}=1.26 V[/tex]