A generator is designed to produce a maximum emf of 170 V while rotating at 3200 rpm. The 1531 coils of the generator are circular with diameter 7.5 cm. What is the necessary magnetic field for the generator?
A) 0.0079 T
B) 0.30 T
C) 0.075 T
D) 0.24 T

Question

Quizplus · Accepted Answer

The maximum emf produced by the generator is given by the equation:
$emf = NBA\omega\sin(\omega t)$
where N is the number of turns, B is the magnetic field, A is the area of the loop, ω is the angular frequency, and t is time.
We are given that emf = 170 V, N = 1531, A = (π/4)(7.5 cm)^2 = 44.18 cm^2 = 0.004418 m^2, and ω = 2π(3200 rpm/60 s/min) = 335.1 rad/s.
Solving for B, we get:
$B = \frac{emf}{N A \omega}$
$B = \frac{170 	ext{ V}}{1531 \cdot 0.004418 	ext{ m}^2 \cdot 335.1 	ext{ rad/s}} = \boxed{0.075	ext{ T}}$
Therefore, the best choice is (C).

A Generator Is Designed to Produce a Maximum Emf of 170