Question

1. A circular loop of radius r is rotating in a uniform external magnetic field of B $xkHMMYA5bipFtu4Y+AAAAAASUVORK5CYII=$ . Find the magnetic flux through the loop due to the external field when the plane of the loop and the magnetic field vectors are oriented at 3 different angles, θ.
2. The coil in an ac generator of frequency f has N turns, each having an area A and is rotated in a uniform magnetic field B $xkHMMYA5bipFtu4Y+AAAAAASUVORK5CYII=$ . What is the peak output voltage of this generator?
3. A piece of equipment is rated with a certain wattage W. What current will it draw when operating from an electric outlet with a potential of V?

Answer 1

Solution) Radius r

Magnetic field B

Magnetic flux = ?

Magnetic flux = B.A = B.(pi)(r^2)

For 3 axes

Magnetic flux = ((Bx)(i) + (By)(j) + (Bz)(k))(pi)(r^2)

Solution) Frequency f

Turns N

Area A

Magnetic field B

Peak voltage , Vmax = ?

V = - d(phi)/dt

Phi = NB.A = NBAcos(wt)

d(phi)/dt = NBAd(cos(wt))/dt

d(phi)/dt = NBAwsin(wt)

For maximum voltage sin(wt) = 1

Vmax = NBAw

w = 2(pi)(f)

Vmax = NBA(2(pi)f)

Solution) Power W

Voltage V

Current i

P = Vi

i = (P/V)