What kinetic energy should a proton have in order to move along an arc of a circle with a radius of 4 cm
| September 4, 2021 | education
What kinetic energy should a proton have in order to move along an arc of a circle with a radius of 4 cm in a uniform magnetic field with an induction of 250 mT?
q = 1.6 * 10-19 Cl.
B = 250 mT = 0.25 T.
R = 4 cm = 0.04 m.
W -?
The kinetic energy of the proton W is determined by the formula: W = m * V2 / 2, where m is the mass of the proton, V is the speed of the proton.
The proton is affected by the Lorentz force: F = q * V * V.
m * V2 / R = q * V * B – 2 Newton’s law.
We express the proton velocity V by the formula: V = q * B * R / m.
W = (q * B * R) 2/2 * m.
W = (1.6 * 10-19 C * 0.25 T * 0.04 m) 2/2 * 1.67 * 10-27 kg = 7660 * 10-19 J = 4787.5 eV = 4.7 keV.
Answer: a proton has a kinetic energy of W = 4.7 keV.
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