# Q6.14 (e) 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 $rod=15cm$ , $B=0.50T$, resistance of the closed loop containing the $rod=9.0m\Omega$ . Assume the field to be uniform. Suppose K is open and the rod is moved with a speed of $12cm\: s^{-1}$ in the direction shown. Give the polarity and magnitude of the induced emf.(e) How much power is required (by an external agent) to keep the rod moving at the same speed   $(=12cm\: s^{-1})$   when $K$is closed? How much power is required when $K$ is open?

Force on the rod

$F=7.5*10^{-2}$

Speed of the rod

$v=12cm/s=0.12m/s$

Power required to keep moving the rod at the same speed

$P=Fv=7.5*10^{-2}*0.12=9*10^{-3}=9mW$

Hence required power is 9mW.

When the key is open, no power is required to keep moving rod at the same speed.

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