First slide

Motional EMF

Question

A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of

Moderate

A

$\frac{mgR}{Bl}$
B

$\frac{mgR}{B^{2} l^{2}}$
C

$\frac{mgR}{B^{3} l^{3}}$
D

$\frac{mgR}{B^{2} l}$

Solution

Due to magnetic field, wire will experience an upward force $F = Bil = B (\frac{Bvl}{R}) l \Rightarrow F = \frac{B^{2} {vl}^{2}}{R}$
If wire slides down with constant velocity, then
$F = mg \Rightarrow \frac{B^{2} {vl}^{2}}{R} = mg \Rightarrow v = \frac{mgR}{B^{2} l^{2}}$

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