Question

A proton enters a uniform magnetic field that is perpendicular

to the proton's velocity (Fig. 20-51).What happens
to the kinetic energy of the proton?
(a) It increases.
(b) It decreases.
(c) It stays the same.
(d) It depends on the velocity direction.
(e) It depends on the B field direction.

Answer 1

When a proton enters a magnetic field perpendicular to its velocity, its kinetic energy remains constant as the magnetic force causes circular motion without changing the speed of the proton.

Step-by-step explanation:

When a proton enters a uniform magnetic field perpendicular to its velocity, the kinetic energy of the proton stays the same. This outcome occurs because the magnetic field exerts a force on the proton that is always perpendicular to its velocity, not altering the speed of the proton but only changing its direction. The proton experiences a centripetal force, which causes circular motion without any change in the speed of the proton. Since kinetic energy is proportional to the square of velocity (and hence, speed), and the speed remains constant in magnitude, the kinetic energy does not change.