- (a) Maximum emf: 90 V (2 sig. fig.)
- (b) Emf at π/32 s: 85 V.
- (c) t = 0.125 s.
<h3>Explanation</h3><h3>(a)</h3>
The maximum emf in the coil depends on
- the maximum flux linkage through the coil, and
- the angular velocity of the coil.
Maximum flux linkage in the coil:
.
Frequency of the rotation:
.
Angular velocity of the coil:
.
Maximum emf in the coil:
.
<h3>(b)</h3>
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.
.
<h3>(c)</h3>
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
.
.