Question

A square loop of side 12 cm with its sides parallel to X and Y axes is moved with a velocity of 8 cm s⁻¹ in the positive x-direction in an environment containing a magnetic field in the positive z-direction. The field is neither uniform in space nor constant in time. It has a gradient of 10⁻³ T cm⁻¹ along the negative x-direction (that is it increases by 10^{− 3} T cm⁻¹ as one moves in the negative x-direction), and it is decreasing in time at the rate of 10⁻³ T s⁻¹. Determine the direction and magnitude of the induced current in the loop if its resistance is 4.50 mΩ.

Answer 1

Side of the square loop, s = 12 cm = 0.12 m
Area of the square loop, A = 0.12 × 0.12 = 0.0144 m²
Velocity of the loop, v = 8 cm/s = 0.08 m/s
Gradient of the magnetic field along negative x-direction,

Rate of change of the flux due to explicit time variation in field B is given as:

Since the rate of change of the flux is the induced emf, the total induced emf in the loop can be calculated as:

Hence, the direction of the induced current is such that there is an increase in the flux through the loop along positive z-direction.