Question

A coil with circular cross section and 18 turns is rotating at a rate of 370 rpm (revolutions per minute) between the poles of a magnet. If the magnetic field strength is 0.7 T and peak voltage is 0.7 V, what is the radius of the coil (in cm)?

Answer 1

r= 2.1 cm

Step-by-step explanation:

Given that

N= 18 turns

N= 370 rpm

B= 0.7 T

V= 0.7 V

The flux given as

Φ = B N A cosωt

B=Magnetic filed

N==Number of turns

A=Area

ω=Speed

t= time

The voltage V give as

`V=-(d\phi)/(dt)`

Φ = B N A cosωt

`(d\phi)/(dt)=BNA\omega\ sin\omegat`

V= BNA ω sinωt

The maximum value of voltage

V(max)= BNA ω

We know that ω=2 πf

`\omega=(2\pi N)/(60)`

`\omega=(2\pi * 370)/(60)`

ω = 38.74 rad/s

A=π r²

V(max)= BNA ω

0.7 = 0.7 x 18 x π r² x 38.74

r²=4.56 x 10⁻⁴ m²

r=0.021 m

r= 2.1 cm