The Compact Muon Solenoid (CMS) is one of the two particle detectors of general

Question

The Compact Muon Solenoid (CMS) is one of the two particle detectors of general purpose in the Large Hadron Collider (LHC) that collisions protons in the CERN, in Switzerland. In its construction, 2600 people have collaborated coming from 180 different scientific institutes. It is situated in the caverns in Cessy, France. It has a cylindrical form of 21 meters of length and 16 meters of width with a weight of 12,500 tons. If the magnetic field generated by the CMS is approximately 100,000 times that of the Earth and the inductance of the solenoid magnet is approximately 14H, Determine: a) the magnetic field in Teslas, b) the number of loops (N), c) the electric current, d) the magnetic energy of the CMS, and e) the density of energy in the magnetic field

Explanation / Answer

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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