Question

A rectangular coil of 65 turns, dimensions 0.100 m by 0.200 m, and total resistance 10.0 ? rotates with angular speed 29.5 rad/s about the y axis in a region where a 1.00-T magnetic field is directed along the x axis. The time t = 0 is chosen to be at an instant when the plane of the coil is perpendicular to the direction of B with arrow.

(a) Calculate the maximum induced emf in the coil.
V

(b) Calculate the maximum rate of change of magnetic flux through the coil.
Wb/s

(c) Calculate the induced emf at t = 0.050 0 s.
V

(d) Calculate the torque exerted by the magnetic field on the coil at the instant when the emf is a maximum.
N

Answer 1

Step-by-step explanation:

N = 65

Area, A = 0.1 x 0.2 = 0.02 m^2

R = 10 ohm

ω = 29.5 rad/s

B = 1 T

(a) at t = 0

e = N x B x A x ω

e = 65 x 1 x 0.02 x 29.5

e = 38.35 V

(b) The maximum rate of change of magnetic flux is equal to the maximum value of induced emf.

Ф = 38.35 Wb/s

(c) e = NBAω Sinωt

e = 65 x 1 x 0.02 x 29.5 x Sin (29.5 x 0.05)

e = 38.174 V

(d) Maximum torque

τ = M B Sin 90

τ = N i A B

τ = N e A B / R

τ = 65 x 38.35 x 0.02 x 1 / 10

τ = 5 Nm