A circular wire has current density J = 2 × 10 10 A m 2 r 2 where r is the radial distance, out of the wire radius is 2   mm . The end-to-end potential applied to the wire is 50   V . How much energy (in joule) is converted to thermal energy in 100   s ?

Step-by-step solution

Given: Current density J = 2 × 10 10 r 2   A   m - 2   , potential V = 50   V , time t = 100   s Energy is given as E = V I t Current I = ∫ 0 2 × 10 - 3 J d A = ∫ 0 2 × 10 - 3 2 × 10 10 r 2 × 2 π r   d r (Since A = 2 π r ) I = 2 × 10 10 2 π ∫ 0 2 × 10 - 3   r 3   d r = 4 π × 10 10 r 4 4 2 × 10 - 3 E = V I t = 50 × 16 π × 100 = 800 π .