The energies required to set up in a cube of side 10 ~cm (i) a uniform electric field of 10^7 Vm ⁻¹ and (ii) a uniform magnetic field of 0.25 Wbm ⁻² are respectively about ( ₀=4 10⁻⁷ Hm ⁻¹, ₀=8.9 10⁻¹² Fm ⁻¹ )

Step-by-step solution

Energy densities are u_E= 1 2 ₀ E^2 u_B= 1 2 B^2 ₀ So, energy required to setup a uniform electric field in cube of side 10 ~cm is aligned U_E & =u_E Volume of cube = 1 2 ₀ E^2 l^3 & = 1 2 8.9 10⁻¹² (10^7 )^2 (0.1)^3 & =4.45 10⁻¹²⁺¹⁴⁻³ & =4.45 10⁻¹=0.445 ~J aligned and energy required to setup a uniform magnetic field in cube of side 10 ~cm is aligned U_B & =u_B Volume of cube & = B^2 l^3 2 ₀ = 0.25 0.25 (0.1)^3 4 10⁻⁷ 2 =25 ~J aligned