a) The magnetic fieldinside a superconducting solenoid is 2.6 T. The solenoid ha

Question

a) The magnetic fieldinside a superconducting solenoid is 2.6 T. The solenoid has aninner diameter of 8.72 cm and a length of 18.4 cm. The permeabilityof free space is 4 × 107 T · m/A.
Determine the magnetic energy density in the field.
Answer in units of J/m3.

b) Determine the energy stored in the magnetic field within thesolenoid.
Answer in units of J. a) The magnetic fieldinside a superconducting solenoid is 2.6 T. The solenoid has aninner diameter of 8.72 cm and a length of 18.4 cm. The permeabilityof free space is 4 × 107 T · m/A.
Determine the magnetic energy density in the field.
Answer in units of J/m3.

b) Determine the energy stored in the magnetic field within thesolenoid.
Answer in units of J.

Explanation / Answer

a ) Magnetic field inside the solenoid is B = 2.6 T                   Magnetic Energy density is   u = B2 /2 0                                                                                             = ( 2.6 T ) 2 / 2 * 4 *10-7                                                                    = 2.69 *106 J / m3 b ) Length of the solenoid is l = 18.4 cm                                                 = 0.184 m            diameter d = 8.72 cm            radius r = 4.36 cm                            = 4.36 *10-2 m        self inductance of thesolenoid is L = 0 N r /l                                                               = 4 * 10-7 * 1 * 4.36 *10-2 m                                                              = 2.976 H                 magnetic field   B = 0 i                                      2.6 T = 4 *10-7 * i                                         i = 2.07*106 A            Energy stored E = 1 / 2 L * i2                                          = 1 / 2 * 2.976 H *( 2.07*106 A)2                                            = 6.376 *1012 J

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