The magnetic field inside a superconducting solenoid is 4.0 T.The solenoid has an inner radius of 3.2 cm and a length of 25.0 cm.Determine (a) the magnetic energy density in the field and (b) the energystored in the magnetic field within the solenoid.diagram must be inclded if needed please

Question
Asked Oct 14, 2019

The magnetic field inside a superconducting solenoid is 4.0 T.
The solenoid has an inner radius of 3.2 cm and a length of 25.0 cm.
Determine (a) the magnetic energy density in the field and (b) the energy
stored in the magnetic field within the solenoid.

diagram must be inclded if needed please

check_circleExpert Solution
Step 1

Given:

Magnetic field inside a solenoid = 4 T

Inner radius of the solenoid, r = 3.2 cm = 0.032 m

Length of the solenoid, L = 25 cm = 0.25 m

Step 2

Calculating the magnetic energy density in the field:

в2
Equation for the magnetic energy density in the field, U =-
2HO
Given magnetic field, B = 0.4 T
is the permeability of free space. 4, = 47Tx10
T m/A
(4 T)2
2(4Tx107 T m/A)
Substituting values, U
6.37MJ
U= 6.37MJ.(1)
Energy density of the magnetic field is U 6.37 MJ
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в2 Equation for the magnetic energy density in the field, U =- 2HO Given magnetic field, B = 0.4 T is the permeability of free space. 4, = 47Tx10 T m/A (4 T)2 2(4Tx107 T m/A) Substituting values, U 6.37MJ U= 6.37MJ.(1) Energy density of the magnetic field is U 6.37 MJ

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Step 3

Calculating the magnetic energy stored in th...

Equation for magnetic energy stored in the field, E = UV
Where V (2L
Substituting the values of radius and length of the solenoid and value of U from eq 1,
E (6.37x10 J)(3.14x(0.032))x 0.25
E 5.12 KJ
help_outline

Image Transcriptionclose

Equation for magnetic energy stored in the field, E = UV Where V (2L Substituting the values of radius and length of the solenoid and value of U from eq 1, E (6.37x10 J)(3.14x(0.032))x 0.25 E 5.12 KJ

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