Question

A uniform and straight wire of length 367 mm is moved at a

constant speed of 14.8 m/s perpendicular to its length and to a
uniform magnetic field.
The e.m.f. generated in the wire is 1.1 V. The wire forms part of a
closed circuit having a total conductance of 139 S.
Calculate the force, F, acting on the wire.

Answer 1

The force acting on the wire is 0.0015 N.

The force acting on the wire can be determined using the formula for electromotive force (emf) in a moving conductor within a magnetic field. The emf (E) is given by Faraday's law as E = B * L * v, where B is the magnetic field strength, L is the length of the wire, and v is the velocity of the wire perpendicular to the magnetic field.

In this scenario, the emf is given as 1.1 V, the velocity is 14.8 m/s, and the length of the wire is 0.367 m (converted from 367 mm). Rearranging the formula to solve for the magnetic field strength (B), we get B = E / (L * v).

Substituting the given values, B = 1.1 V / (0.367 m * 14.8 m/s) ≈ 0.205 T.

To calculate the force (F) acting on the wire, we use the formula F = B * I * L, where I is the current and L is the length of the wire. Since the wire is part of a closed circuit, the current (I) is given by Ohm's Law as I = E / R, where R is the total conductance.

Substituting the values, I = 1.1 V / 139 S ≈ 0.00791 A.

Now, F = 0.205 T * 0.00791 A * 0.367 m ≈ 0.0015 N.

Therefore, the force acting on the wire is approximately 0.0015 N.