The large hardon collider at CERN accelerates protons to speeds over 99% the spe

Question

The large hardon collider at CERN accelerates protons to speeds over 99% the speed of light (3.00E8 m/s). The protons travel through an underground tunnel around a large circle with a circumference of 27 km. The protons are steered around the circle with large magnets tut produce a uniform magnetic field in the beam's path. Consider a beam of protons traveling around the collider at 80% the speed of light. A. What must the magnetic field strength of the steering magnets be? B. Assume that when viewed from above, the protons travel around the collider counter-clockwise. What direction must the magnetic field used to steer the beam point? C. The bean of electrons is a current, and will therefore create a magnetic field as well. Assume the current of the beam is 100kA. What is the strength of the magnetic field due to the current at the center of the collider ring (I.e. The center of the large circle the protons travel around)? The large hardon collider at CERN accelerates protons to speeds over 99% the speed of light (3.00E8 m/s). The protons travel through an underground tunnel around a large circle with a circumference of 27 km. The protons are steered around the circle with large magnets tut produce a uniform magnetic field in the beam's path. Consider a beam of protons traveling around the collider at 80% the speed of light. A. What must the magnetic field strength of the steering magnets be? B. Assume that when viewed from above, the protons travel around the collider counter-clockwise. What direction must the magnetic field used to steer the beam point? C. The bean of electrons is a current, and will therefore create a magnetic field as well. Assume the current of the beam is 100kA. What is the strength of the magnetic field due to the current at the center of the collider ring (I.e. The center of the large circle the protons travel around)? A. What must the magnetic field strength of the steering magnets be? B. Assume that when viewed from above, the protons travel around the collider counter-clockwise. What direction must the magnetic field used to steer the beam point? C. The bean of electrons is a current, and will therefore create a magnetic field as well. Assume the current of the beam is 100kA. What is the strength of the magnetic field due to the current at the center of the collider ring (I.e. The center of the large circle the protons travel around)?

Explanation / Answer

radius of the circle, r = 27 km/(2*pi)

= 4.297 km

speed of charged particle, v = 80% 0f c

= 0.8*3*10^8

= 2.4*10^8 m/s

a) Apply, F = q*v*B

m*a = q*v*B

m*v^2/r = q*v*B

==> B = m*v/(r*q)

= 1.67*10^-27*2.4*10^8/(4.297*10^3*1.6*10^-19)

= 5.83*10^-4 T

b) direction of B is downward (in to the ground)

c) apply, at the cnetre of the ring, B = mue*I/(2*r)

= 4*pi*10^-7*100*10^3/(2*4.297*10^3)

= 1.46*10^-2 T

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