23.5 Electric Generators

The emf induced in a coil that is rotating in a magnetic field will be at a maximum when

1. the magnetic flux is at a maximum.
2. the magnetic flux is at a minimum.
3. the change in magnetic flux is at a maximum.
4. the change in magnetic flux is at a minimum.

Calculate the peak voltage of a generator that rotates its 200-turn, 0.100 m diameter coil at 3600 rpm in a 0.800 T field.

What is the peak emf generated by rotating a 1000-turn, 20.0 cm diameter coil in the Earth’s $5 . \text{00} \times \text{10}^{- 5} \text{T}$ magnetic field, given the plane of the coil is originally perpendicular to the Earth’s field and is rotated to be parallel to the field in 10.0 ms?

(a) A bicycle generator rotates at 1875 rad/s, producing an 18.0 V peak emf. It has a 1.00 by 3.00 cm rectangular coil in a 0.640 T field. How many turns are in the coil? (b) Is this number of turns of wire practical for a 1.00 by 3.00 cm coil?

(a) A car generator turns at 400 rpm when the engine is idling. Its 300-turn, 5.00 by 8.00 cm rectangular coil rotates in an adjustable magnetic field so that it can produce sufficient voltage even at low rpms. What is the field strength needed to produce a 24.0 V peak emf? (b) Discuss how this required field strength compares to those available in permanent and electromagnets.

A 75-turn, 10.0 cm diameter coil rotates at an angular velocity of 8.00 rad/s in a 1.25 T field, starting with the plane of the coil parallel to the field. (a) What is the peak emf? (b) At what time is the peak emf first reached? (c) At what time is the emf first at its most negative? (d) What is the period of the AC voltage output?

A 500-turn coil with a $0 . \text{250} \text{m}^{2}$ area is spun in the Earth’s $5 . \text{00} \times \text{10}^{- 5} \text{T}$ field, producing a 12.0 kV maximum emf. (a) At what angular velocity must the coil be spun? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?