A rectangular loop with a sliding connector of length l = 1.0 ,m … - Vidyadip

Question

A rectangular loop with a sliding connector of length $l = 1.0 \,m$ is situated in a uniform magnetic field $B = 2\,T$ perpendicular to the plane of loop. Resistance of connector is $r = 2$ $\Omega$ Two resistance of $6$ $\Omega$ and $3$ $\Omega$ are connected as shown in figure. The external force required to keep the connector moving with a constant velocity $v = 2\,m/s$ is........$N$

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Answer

(c) Motional emf $e = Bvl \Rightarrow e = 2 \times 2 \times 1 = 4\;V$
This acts as a cell of emf $E = 4\;V$and internal resistance $r = 2\Omega $.
This simple circuit can be drawn as follows

Current through the connector $i = \frac{4}{{2 + 2}} = 1\;A$
magnetic force on connector${F_m} = Bil = 2 \times 1 \times 1 = 2\;N$
(Towards left)

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