A 10.0-cm-long wire is pulled along a U-shaped conducting rail in a perpendicular magnetic field. The total resistance of the wire and rail is 0.300 Ω . Pulling the wire at a steady speed of 4.00 m/s causes 3.90 W of power to be dissipated in the circuit.

Question:

What are the magnitudes of the  pulling force and the magnetic field

The magnetic field strength is 2.7 T

The pulling force is 0.975 N

Explanation:

Here we have;

Length of wire, l = 10.0 cm = 0.1 m

Resistance of wire, R = 0.300 Ω

Speed of wire, v = 4.00 m/s

Power dissipated = 3.90 W

Based on the given data, we apply the relation;

..............(1)

Where:

B = Magnetic field strength

I = Current

Since P = I²R, we have;

3.9 = I²·0.300Ω

∴ I² = 3.9/0.300 = 13

From which I = √13

Substituting the value of I in equation (1) above, we have;

Therefore;

The magnitude of the pulling force is given by the following relation;

The pulling force = 0.975 N.