A generator has a 100-turn coil that rotates in a 0.30-T magnitude B-field at a frequency of 80 Hz. The area of each loop is 0.003 m2. Assume the coil plane is parallel at time is equal to 0. Determine the emf magnitude (in V) when time is 0.0140 s. Use 3 significant figures for answer.

Explanation:

Flux Φ = nBA sinωt

t = 0 , flux = 0

dΦ / dt = nωBA Cosωt

e = nωBA Cosωt

= 100 x 2πx80 x.3 x .003 cos 2πx80 x .014

= 45.21 cos 7.0336

= 33.0668 v

= 33.1 V

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west