Question

Part A What magnetic field B is needed to keep 999-GeV protons revolving in a circle of radius 2.0 km ? Use the relativistic mass. The proton's "rest mass" is 0.938 GeV/c2 1 GeV - 10 eV) [Hint: In relativity, mrelvr-quB in still valid in a magnetic field, mrel-m Express your answer to two significant figures and include the appropriate units B-Value Units Submit Request Answer

Answer 1

Energy of proton,

E = KE + m_pc^2

E = 999 + 0.938 = 999.938 GeV

Relative mass, m_rel= $\gamma$ m_p

999.938 = $\gamma$ * 0.938

$\gamma$ = 1066.03

From equilibrium of force,

qvB = m_rel * v^2 / r

B = m_rel * v / qr = $\gamma$ *m_p v / qr

B = 1066.03 * 1.67*10^-27 * 3*10⁸ / 1.6*10^-19 * 2*10³

B = 1.669 T

Magnetic field B = 1.669 T