In Figure P31.40, a semicircular conductor of radius R 5 0.250 m is rotated abou

Question

In Figure P31.40, a semicircular conductor of radius
R 5 0.250 m is rotated about the axis AC at a constant rate
of 120 rev/min. A uniform magnetic field of magnitude
1.30 T fills the entire region below the axis and is directed
out of the page. (a) Calculate the maximum value of the
emf induced between the ends of the conductor. (b) What
is the value of the average induced emf for each complete
rotation? (c) What If? How would your answers to parts
(a) and (b) change if the magnetic field were allowed to
extend a distance R above the axis of rotation? Sketch the
emf versus time (d) when the field is as drawn in Figure
P31.40 and (e) when the field is extended as described in
part (c).

Explanation / Answer

a)

Induced Emf is given by :

E = BAW <-----maximum value

where B = magnetic field = 1.3 T

A = area of the loop = pi*R^2/2 = pi*0.25^2/2

W = angular speed of rotation = 120 rev/min = 120*2*pi/60 = 4*pi rad/s

So, E = 1.3*(pi*0.25^2/2)*4*pi = 1.6 V <-------answer

b)

Average emf, Eav = 0

c)

When it is extended ,

answer to part (a) will be same as before = 1.6 V

for part (b) answer will be : 0

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