What magnetic field is needed to keep 963-GeV protons revolving in a circle of r

Question

What magnetic field is needed to keep 963-GeV protons revolving in a circle of radius 5.0km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass is 0.938GeV/c 2. (1GeV=10 9 eV). [Hint: In relativity, m rel v 2 /r=qvB is still valid in a magnetic field, where m rel =m.]

I have worked through the problem from previous answers and for some reason I am having trouble with this problem, please help.

What magnetic field is needed to keep 963-GeV protons revolving in a circle of radius 5.0km km (at, say, the Fermilab synchrotron)? Use the relativistic mass. The proton's rest mass is 0.938GeV/ c 2. (1GeV =10 9 eV ). [Hint: In relativity, m rel v 2 / r=qvB is still valid in a magnetic field, where m rel = .]

Explanation / Answer

we know from the relation

mv^2/r = q x v x B

or mv/r = q x B

or B = (mv/r x q) ------------(1)

where B is magnetic field,m is mass of proton(1.67 x 10^-27 kg),v is speed of proton,r is radius(5.0 km = 5.0 x 10^3 m) and q = +1.6 x 10^-19 C

the kinetic energy of protons is K = 963 GeV = 963 x 10^9 eV = 963 x 10^9 x 1.6 x 10^-19 J

we know that

K = (1/2)mv^2

or v^2 = (2K/m)

or v = (2K/m)^1/2 -----------(2)

from equations (1) and (2) we get

B = (m x (2K/m)^1/2/r x q) = ((2K x m)^1/2/r x q)

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