A circular conducting coil of radius 1   m is being heated by the change of magnetic field B → passing perpendicular to the plane in which the coil is laid. The resistance of the coil is 2   μΩ . The magnetic field is slowly switched off such that its magnitude changes in time as B = 4 π × 10 - 3   T 1 - t 100 The energy dissipated by the coil before the magnetic field is swit

Step-by-step solution

ϕ = B → · S → ϕ = 4 π × 10 - 3 1 - t 100 · π R 2 ϕ = 4 × 10 - 3 × 1 2 1 - t 100 ε = - d ϕ d t ε = - d d t 4 × 10 - 3 1 - t 100 ε = 4 × 10 - 3 1 100 = 4 × 10 - 5   V When B = 0 1 - t 100 = 0 t = 100   sec Heat = ε 2 R t Heat = 4 × 10 - 5 2 2 × 10 - 6 × 100   J Heat = 16 × 10 - 10 × 100 2 × 10 - 6   J Heat = 0 . 08   J Heat = 80   mJ