. Assume the
field to be uniform.
(a)
Suppose K is open and the rod is moved with a speed of 12 cm 
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 
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?
Answer:
(a) Using 
,
we get
The
electrons in the rod will experience force along PQ, so end P becomes positive
and Q becomes negative.
(b)
Yes. On closing the key K the number of electrons become more at end O.
Therefore, excess charge is maintained by the continuous current.
(c)
Magnetic force gets cancelled by electric force due to excess charges of
opposite sign at the ends of the rod.
(d)
Retarding force, 
(e)
Power, 
When
K is open no power is spent.
(f)
Power lost 
The
source of this power is the external agency.
(g)
Zero, because motion of rod does not cut or link with field lines.
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