The Compact Muon Solenoid is one of two particle detectors for general purpose o

Question

The Compact Muon Solenoid is one of two particle detectors for general purpose of the Large Hardon Collider. It is situated in Cave Cessy and has a cilindrical it is 21m long 16m across and with a weight of 12.500 tons. If the magnetic field generated by CMS is approximately 100,000 times that of earth and the inductance of the magnet is approximately 14H determine:
(1) the magnetic field in teslas
(2) number of round trips

(3) the elctric current

(4) the magnetic energy of the CMS

(5)the density of energy in a magnetic field

Explanation / Answer

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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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