A rigid square conducting loop of side length 20 cm and resistance 2 m is pulled with a constant velocity of 10 cm s ⁻¹ in the positive x -direction. The space contains a magnetic field directed along the positive z -direction. The magnetic field is increasing with time at a rate of 5 mT s ⁻¹ , and it also has a uniform spatial gradient of 0.5 T m ⁻¹ along the positive x -direction. The magnitude of the external mech

Step-by-step solution

Let the side length of the square loop be a = 20 cm = 0.2 m . Area of the loop, A = a^2 = 0.04 m ^2 . The rate of change of magnetic flux through the loop has two components: 1. Due to the motion of the loop in a spatially varying field (motional EMF): _ mot = A v B x = 0.04 0.1 0.5 = 2 10⁻³ V 2. Due to the explicit time variation of the magnetic field: _ time = A B t = 0.04 (5 10⁻³) = 0.2 10⁻³ V Since the loop moves in the +x direction (where B is increasing) and the field itself is increasing with time, both effe