13.2 Problems
597
13.74 A uniform magnetic field of induction B fills a cylindrical volume of radius
R. A metal rod of length 2l is placed as in Fig. 13.18. If dB/dt is the rate of
change of B show that the emf that is produced by the changing magnetic
field that acts at the ends of the rod is given by
ξ = −
dB
dt
l
R 2 − l 2
Fig. 13.18 Magnetic
induction at the centre of a
current-carrying wire made of
three-fourths of a circle and a
chord
13.75 A square wire of length l, mass m and resistance R slides without friction
on parallel conducting resistance rails as in Fig. 13.19. The rails are interconnected at the bottom by resistance rails so that R, the wire and rails form
a closed rectangular loop. The plane of the rails is inclined at an angle θ
with the horizontal and a vertical uniform magnetic field B exists within the
frame. Show that the wire acquires a steady velocity of magnitude
v =
mgR sin θ
B 2 l 2 cos 2 θ
Fig. 13.19
13.76 A copper disc of 10 cm radius makes 1200 rotations per minute with its plane
perpendicular to a magnetic field. If the induced emf between the centre and
the edge of the disc is 6.28 mV, find the intensity of the field.
[Indian Administrative Services]