A loop antenna of area A = 3.25 cm2 and resistance R = 7.17 μΩ is perpendicular to a uniform magnetic field of magnitude 20.2 μT. The field magnitude drops to zero in 2.03 ms. How much thermal energy is produced in joules in the loop by the change in field?

change in flux = area x change in magnetic field

= 3.25 x 10⁻⁴ x (20.2 - 0) x 10⁻⁶

= 65.65 x 10⁻¹⁰ Weber.

emf induced = change in flux / time

= 65.65 x 10⁻¹⁰ / 2.03 x 10⁻³

= 32.34 x 10⁻⁷ V

current = volt induced / resistance

= 32.34 x 10⁻⁷ / 7.17 x 10⁻⁶

=.451 A

Thermal energy produced = I²R t, I is current, R is resistance, t is time

=.451² x 7.17 x 10⁻⁶ x 2.03 x 10⁻³

= 2.96 x 10⁻⁹ J.