A toy electric generator has a 20-turn circular coil with each turn of radius 1.

Question

A toy electric generator has a 20-turn circular coil with each turn of radius 1.8 cm. The coil resides in a 1.0-T magnitude B field. It also has a lightbulb that lights if the potential difference across it is about 1 V. You start rotating the coil, which is initially perpendicular to the B field. Determine the time interval needed for a 90 rotation that will produce an average induced emf of 1.0 V.

If the time interval for one rotation is reduced by one-fourth while the radius of the coil is reduced by one-half, how will emf change?

a. E in new=1/2×E in old. b. E in new=1/4×E in old. c. E in new=E in old. d. E in new=2×E in old. e. E in new=4×E in old.

Explanation / Answer

induced emf is defiend as the rate of change of magnetic flux

in mathematical form,

induced emf e = NAdB/dt or NABW

where A = area

N = no. of tunrs

W = angular frequency

dB/dt = rate of change of amgnetic flux

so time dt = NAdB/emf

dt = 20 * 3.14 * 0.018 * 0.018 * 1 /1

dt = 0.0203 secs

---------------------

r = = 1.8/2 = 0.9 cm

dt = 0.0203/4 = 0.00508 secs

so

new emf e = 20 * 3.14 *0.009 * 0.009 * 1/(0.00508)

new emf = 1

new emf = E old , option C it is

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