A conducting rod of length 20 cm undergoes pure translation at a uniform velocity of 10 cm s ⁻¹ perpendicular to its length. A uniform magnetic field of 0.10 T is present, directed perpendicular to the plane of motion. What electric field inside the rod will cause the electric force on a free electron to balance the magnetic force?

Step-by-step solution

The magnetic force acting on a free electron in the moving rod is given by F_ m = e v B . The electric force acting on the electron due to the induced electric field is F_ e = e E . For the forces to balance, F_ e = F_ m : e E = e v B E = v B Substituting the given values, v = 10 cm s ⁻¹ = 0.1 m s ⁻¹ and B = 0.10 T : E = 0.1 0.10 = 0.01 Vm ⁻¹ = 1.0 10⁻² Vm ⁻¹