Magnetic field

A square wire loop having side length aa, mass mm, and resistance RR is moving along the positive xx-axis at a speed of v0v_0. It enters a uniform, steady magnetic field B=B0(k^)\vec B = B_0 \big(-\widehat k \big) at t=0t = 0 seconds, as shown in the figure.

Find the total amount of heat loss in the resistance.

Details and Assumptions:

  • The magnitude of v0v_0 is sufficient that the loop comes out of the region of magnetic field with some speed.

  • Neglect any type of energy loss other than the heat loss in resistance of the wires of the square.

  • Take v0=3B2a3mR v_0 = \dfrac{3B^2 a^3}{mR} .

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