1.

Figure6.20 shows a metal rod PQ resting on the smooth rails AB andpositioned between the poles of a permanent magnet. The rails, therod, and the magnetic field are in three mutual perpendiculardirections. A galvanometer G connects the rails through a switch K.Length of the rod = 15 cm, B =0.50 T, resistance of the closed loop containing the rod = 9.0mΩ. Assumethe field to be uniform.(a) SupposeK is open and the rod is moved with a speed of 12 cm s−1in the direction shown. Give the polarity and magnitude of theinduced emf.(b) Isthere an excess charge built up at the ends of the rods whenKis open? What if K is closed? (c) With Kopen and the rod moving uniformly, there is nonet force on the electrons in therod PQ even though they do experience magnetic force due to themotion of the rod. Explain.(d) Whatis the retarding force on the rod when K is closed?(e) Howmuch power is required (by an external agent) to keep the rod movingat the same speed (=12 cm s−1)when K is closed? How much power is required when K is open?(f) Howmuch power is dissipated as heat in the closed circuit?Whatis the source of this power?(g) Whatis the induced emf in the moving rod if the magnetic field isparallel to the rails instead of being perpendicular?

Answer»

Figure
6.20 shows a metal rod PQ resting on the smooth rails AB and
positioned between the poles of a permanent magnet. The rails, the
rod, and the magnetic field are in three mutual perpendicular
directions. A galvanometer G connects the rails through a switch K.
Length of the rod = 15 cm, B =
0.50 T, resistance of the closed loop containing the rod = 9.0
mΩ. Assume
the field to be uniform.




(a) Suppose
K is open and the rod is moved with a speed of 12 cm s−1
in the direction shown. Give the polarity and magnitude of the
induced emf.







(b) Is
there an excess charge built up at the ends of the rods when


K
is open? What if K is closed?




(c) With K
open and the rod moving uniformly, there is no
net force
on the electrons in the
rod PQ even though they do experience magnetic force due to the
motion of the rod. Explain.



(d) What
is the retarding force on the rod when K is closed?



(e) How
much power is required (by an external agent) to keep the rod moving
at the same speed (=12 cm s−1)
when K is closed? How much power is required when K is open?



(f) How
much power is dissipated as heat in the closed circuit?


What
is the source of this power?



(g) What
is the induced emf in the moving rod if the magnetic field is
parallel to the rails instead of being perpendicular?



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