The Large Hadron Collider (LHC) is a roughly circular track of circumference abo
ID: 3279411 • Letter: T
Question
The Large Hadron Collider (LHC) is a roughly circular track of circumference about 27.0 km. Protons with mass 0.9383 Gev/c^2 and charge e circle around it in both directions. (a) To keep the protons going in a circle, there is presumably a field present. For protons going clockwise, as viewed from above, this field must be oriented in the direction. (b) The LHC can operate at up to 7 TeV. When it is working at 5.600 TeV, what is the momentum of the protons? P = TeV/c (c) What must be the strength of the fields at this energy? Give your answer in Tesla T = V s/m^2. B = T Comment: The actual magnets must be stronger than this, because they operate at higher energy and alternate with smaller regions which lack strong magnetic fields. They have a maximum magnetic field of about 8.26 T.Explanation / Answer
(a) For protons moving in a circle, there must be a magnetic field present as magnetic field exerts a force which is perpendicular to velocity of charged particle and acts like a centripetal force, making the charged particle move in a circle.
Protons are moving in counterclockwise direction. Let at any instant their velocity is directed in left direction. Then force due to magnetic field acts in perpendicular direction to velocity of proton. This force acts towards the center of circle in which proton is moving. Applying Fleming's left hand rule, thumb is in direction of force, central finger in direction of velocity, then index finger gives direction of magnetic field. It gives downward (into the Earth) direction.
(b) E2 = (p.c)2 + Eo2
(5.6TeV)2 = (p.c)2 + (moc2)2where moc2= rest mass energy = 0.9383 GeV/c2x c2= 0.9383 GeV
= 0.9383 x 10-3 TeV
(5.6 TeV)2 = p2c2 + (0.9383 x 10-3 TeV)2
(5.6TeV)2 - (0.9383 x 10-3 TeV)2 = p2c2
31.36 (TeV)2 = p2c2
p = 5.60 TeV/c
(c) qvB = 5.6 TeV
where q = 1.6 x 10-19 C, B = ? and v could be found using momentum
p = mov/(1-v2/c2)1/2
v = 0.999999974c
1.6 x 10-19 x 0.999999974 x 3 x 108 x B = 5.6 x 1012 x 1.6 x 10-19
B = 18666.67 T
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