Answer:
The angular velocity I would have to rotate it in order to generate an emf of amplitude 1.0 V is 254.65 rad/s
Explanation:
given information:
B = 0.5 mT = 0.0005 T
N = 1000
r = 5 cm = 0.05 m
emf, ε = 1 V
according to Faraday's law
ε = -N dΦ/dt, Φ = B A
= - N d( B A)/dt
= - N d( B A cos ωt)/dt
= - N B A d(cos ωt)/dt
= N B A ω sin ωt
A = πr², so
ε = N B πr² ω sin ωt
where
ε = emf
N = number of coil turn
B = magnetic field
r = radius
ω = angular velocity
Φ = magnetic flux
emf maximum, sin ωt = 1. So,
ε = N B πr² ω
ω = ε/N B πr²
= 1/[(1000) (0.0005) π (0.05)²
= 254.65 rad/s
