Consider a variation of the previous problem figure. Suppose the circular loop lies in a vertical plane. The rod has a mass m. The rod and the loop have negligible resistances but the wire connecting O and C has a resistance R. The rod is made to rotate with a uniform angular velocity ω in the clockwise direction by applying a force at the midpoint of OA in a direction perpendicular to it. Find the magnitude of this force when the rod makes an angle θ with the vertical.

Question

Philoid · Accepted Answer

When the circular loop is in the vertical plane, it tends to rotate in the clockwise direction because of its weight.

Let the force applied be F and its direction be perpendicular to the rod.
The component of mg along F is mg sin θ.
The magnetic force is in perpendicular and opposite direction to mg sin θ.

Now, Current in the rod will be

The force on the rod will be

So, the net force will be

The net force passes through the centre of mass of the rod.
Net torque on the rod about the centre O will be

Because the rod rotates with a constant angular velocity, the net torque on it is zero.

Thus,