As shown in figure, a metal rod completes the circuit. The circuit area is perpendicular to a magnetic field with `B = 0.15 T`. If the resistance of the total circuit is `3 Omega`, how large a force is needed to move the rod as indicated with a constant speed of 2 m/s?

Options

A. `3.75xx10^(-3)N`
B. `3.75xx10^(-2)N`
C. `3.75xx10^(2)N`
D. `3.75xx10^(-4)`

Answer

A

Explanation

Induced current in the circuit `i=(Bvl)/(R )`
Magneticforceactingonthewire `F_(m)=bil=B(Bvl)/(R ))l`
`impliesF_(m)=(B^(2)vl^(2))/(R )` External force needed to move the rod with constant velocity
`(F_(m))=(B^(2)vl^(2))/(R )=((0.15)^(2)xx(2)xx(0.5)^(2))/(3)`
`=3.75xx10^(-3)N`