As shown in the figure a metal rod makes contact and complete the circuit. The circuit is perpendicular to the magnetic field with If the resistance is $$3$$Ω , force needed to move the rod as indicated with a constant speed of $$2m/$$$$sec$$ is

Induced current in the circuit Magnetic force acting on the wire External force needed to move the rod with constant velocity

Force on a current carrying wire placed in a magnetic field

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Question

As shown in the figure a metal rod makes contact and complete the circuit. The circuit is perpendicular to the magnetic field with $B = 0.15\,tesla.$ If the resistance is 3Ω , force needed to move the rod as indicated with a constant speed of 2m/sec is

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Solution

Induced current in the circuit $i = \frac{{Bvl}}{R}$
Magnetic force acting on the wire ${F_m} = Bil = B\left( {\frac{{Bvl}}{R}} \right)\;l$
$\Rightarrow {F_m} = \frac{{{B^2}v{l^2}}}{R}$ External force needed to move the rod with constant velocity
$({F_m}) = \frac{{{B^2}v{l^2}}}{R} = \frac{{{{(0.15)}^2} \times (2) \times {{(0.5)}^2}}}{3} = 3.75 \times {10^{ - 3}}N$

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