a) The magnetic fieldinside a superconducting solenoid is 2.6 T. The solenoid ha
ID: 1675516 • Letter: A
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 JRelated Questions
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