Question

The magnetic field inside a superconducting solenoid is 4.00 T. The solenoid has an inner diameter of 6.20 cm and a length of 26.0 cm.(a) Determine the magnetic energy density in the field.uB = 1 J / m3(b) Determine the energy stored in the magnetic field within the solenoid.UB = 2 kJ

Answer 1

(a) The magnetic energy density in the field is 6.366 J/m³

(b) The energy stored in the magnetic field within the solenoid is 5 kJ

Step-by-step explanation:

magnitude of magnetic field inside solenoid, B = 4 T

inner diameter of solenoid, d = 6.2 cm

inner radius of the solenoid, r = 3.1 cm = 0.031 m

length of solenoid, L = 26 cm = 0.26 m

(a) The magnetic energy density in the field is given by;

`u _B = (B^2)/(2\mu_o) \\\\u _B = ((4)^2)/(2(4\pi*10^(-7)))\\\\u_B = 6.366*10^6 \ J/m^3`

(b) The energy stored in the magnetic field within the solenoid

`U_B = u_B V\\\\U_B = u_B AL`

`U_B = u_B(A)(L)\\\\U_B = 6.366*10^6(\pi * 0.031^2)(0.26) \\\\U_B = 4997.69 J\\\\U_B = 5 \ KJ\\`