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or the future Electron Ion Collider (EIC) a proposed magnet for the detector is a solenoid with the following properties: B = 3 Tesla (assume uniform inside, 0 outside) Length L

or the future Electron Ion Collider (EIC) a proposed magnet for the detector is a solenoid with the following properties: B = 3 Tesla (assume uniform inside, 0 outside) Length L

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or the future Electron Ion Collider (EIC) a proposed magnet for the detector is a solenoid with the following properties:

B = 3 Tesla (assume uniform inside, 0 outside)

Length L = 4.0 m

Inner Radius R = 1.5 m

Use the long thin solenoid approximation of uniform field, even though this is a short squat solenoid

A). Assuming the coil has radius R = 1.5 m, what is the current density (Amp per unit length)

B) Calculate the total stored energy in the magnetic field, in Joules. 
Given that 1 gallon of gasoline contains about 10 8 Joules of chemical energy is this a large, medium, or small amount of stored energy?

C) The coil would be superconducting.  If the coil were to suddenly lose it's superconductivity and the magnetic field ramped down extremely rapidly, where would the stored energy go?

 

Expert Solution
Step 1

solenoid with magnetic field= 3T

Length= 4.0m 

Inner radius=1.5m 

using ampere's circuital law∮ B→.dl→ =μ0 Itot          (1)Itot=nLI                        (2)where n is the number of turns per unit lengthL is the length of the solenoidfrom equation (1) and (2) BL=μ0nLInI=J=the required current density per unit lengthBL=μ0LJJ=Bμ0  =34π×10-7 A/length  =0.24×107 Ampere/length

Answer: current density per unit length= 0.24×107 Ampere/metre

Step 2

Energy stored in the magnetic field

E=B22 μ0×ALA=πr2   =3.14×(1.5)2 m2    =7.065 m2L=4m, B=3TeslaE=32×7.065×42×2π×10-7   =2.025×108 joule

Answer: energy stored in the magnetic field=2.025×108 Joule

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