In a model ac generator, a 505 turn rectangular coil 8.0 cm by 30 cm rotates at 120 rev/min in a uniform magnetic field of 0.59 t.

(a) what is the maximum emf induced in the coil?

(b) what is the instantaneous value of the emf in the coil at t = (π/32) s? assume that the emf is zero at t = 0.

(c) what is the smallest value of t for which the emf will have its maximum value? s

The maximum emf in the coil depends on

Maximum flux linkage in the coil:

.

Frequency of the rotation:

.

Angular velocity of the coil:

.

Maximum emf in the coil:

.

Emf varies over time. The trend of change in emf over time resembles the shape of either a sine wave or a cosine wave since the coil rotates at a constant angular speed. The question states that emf is "zero at t = 0." As a result, a sine wave will be the most appropriate here since .

.

Make sure that your calculator is in the radian mode.

.

Consider the shape of a sine wave. The value of varies between -1 and 1 as the value of changes. The value of at time depends on the value of .

reaches its first maximum for when what's inside the sine function is equal to .

In other words, the first maximum emf occurs when

,

where

,

and

.

.

work: w = fd (given)

work done by chet   =50*1 = 50 j

work done by mika =40*2 = 80 j

work done by sara =30*1.5 = 45 j

work done by bill =60*0.5 = 30 j

students in order from the greatest amount of work done to the least is mika> chet> sara> bill

hence option (b) is correct.