Question

A bar of mass m = 0.200 kg slide without friction on a pair of rails separated by a distance at the length of 1.20 m. The pair of rails was located on an inclined plane making an angle of 25 degrees with respect to the ground. The rails were connected by a resistor at the top of the incline. The resistance of the resistor is R= 1 Ohm, and a uniform magnetic field of magnitude B = 0.500 T is directed downward, perpendicular to the ground, over the entire region through which the bar moved. With what constant speed v did the bar slide along the rails (2 significant figures)?

Answer 1

To solve this problem, we need to consider the fact that the bar is moving with constant speed. That means the net force on the bar is zero. The force acting on the bar are the magnetic force, and the component of its weight downwards along the incline.

To find the magnetic force, we need to find the current through the rod. The only component of the magnetic field that contributes to the force will be the component perpendicular to the velocity and length, the cosine component.

First, we express the EMF due to the bar moving in the magnetic field.

Then, we express the force in terms of the current, and appropriately substitute with the EMF and resistance.

This component of weight along the incline will be

Since these are directed in the opposite direction, the forces will be in equal in magnitude for the bar to be moving with no net force.