Question

Suppose that a proton has a component of velocity parallel to the magnetic field as well as perpendicular to it (Figure 20.80). What is the effect of the magnetic field on this parallel component of the velocity? What will the trajectory of the proton look like?

Short answer

The parallel component of velocity will be unaffected by the magnetic field. The proton will follow a spiral path upwards around the magnetic field.

Step-by-step solution

Given data

A proton has a component of velocity parallel to the magnetic field as well as perpendicular to it.

Magnetic force

Magnetic force on a moving charge is directly proportional to the cross product of the velocity vector and the magnetic field.

Determination of the magnetic effect on the parallel component of the velocity and the net trajectory of the photon

Since the cross products of two parallel vectors is zero, the parallel component of the velocity of the proton along the magnetic field is unaffected by it. The perpendicular component faces the magnetic force and traces a circle around the magnetic field direction. Thus, the proton follows a spiral path with the parallel component moving up and the perpendicular component tracing a circle.