Question

The diameter of a 3.0m long solenoid is 0.80m. the magnetic at its centre is 0.80T.estimate the energy stored in the magnetic field of the solenoid.

Answer 1

The density of energy of the magnetic field

$$u_B=\frac{B^2}{2\mu_0}=\frac{0.8^2}{2*4\pi*10^{-7}}=2.55*10^5\:\rm J/m^3$$

The energy of the magnetic field inside solenoid

$$W_B=u_B*V=u_B*\pi R^2L\\ =2.55*10^5*3.0*3.14*0.4^2=3.84*10^5\:\rm J$$