First slide

Magnetic flux and induced emf

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 $3 Ω$ , force needed to move the rod as indicated with a constant speed of $2 m / \sec$ is

Moderate

A

$3 .75 \times 10^{- 3} N$
B

$3 .75 \times 10^{- 2} N$
C

$3 .75 \times 10^{2} N$
D

$3 .75 \times 10^{- 4} N$

Solution

Induced current in the circuit $i = \frac{Bvl}{R}$
Magnetic force acting on the wire $F_{m} = Bil = B (\frac{Bvl}{R}) l$
$\Rightarrow F_{m} = \frac{B^{2} {vl}^{2}}{R}$ External force needed to move the rod with constant velocity
$(F_{m}) = \frac{B^{2} {vl}^{2}}{R} = \frac{{(0 .15)}^{2} \times (2) \times {(0 .5)}^{2}}{3} = 3 .75 \times 10^{- 3} N$

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