The Compact Muon Solenoid Solenoid (CMS) is one of the two general purpose parti

Question

The Compact Muon Solenoid Solenoid (CMS) is one of the two general purpose particle detectors of the Large Hadron Coater, which collides proton beams at CERN, in Switzerland. Around 2,600 people from 180 different scientific institutes have collaborated in its construction. It is located in the cavern of Cessy (France). It has a cylindrical shape, 21 meters long by 16 wide, weighing 12,500 tons. If the magnetic field generated by the CMS is approximately 100,000 times the magnetic field of the Earth and the inductance of the solenoid magnet is approximately 14H, determine: 
(a) the magnetic field in teslas
(b) the number of turns
(c) the electric current
(d) the magnetic energy of the CMs
(e) the energy density in the magnetic field.

Explanation / Answer

Solution :-

Cylinder shape = 21 m long and wide = 16 m

a)magnetic field of the earth = 31.1 *10^-6 T

so magnetic field = 31.1*10^-6*10^5

=3.11 T

b)let the number of loops be N.so,

N*magnetic flux/I = L

or N*B*A/I = L

or N*3.11*pi*8^2/I = 14 -----(1)

also,

u*n*I = B

or 4*pi*10^-7*N*I/21 = 3.11 -----(2)

solving 1 and 2, we get

N=1078.71 loops

I=48179.9 A

c)I = 48179.9 A

d)magnetic energy = 0.5*L*i^2

=0.5*14*48179.9^2

=1.62*10^10 J

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