What is the speed of the proton?

Question

A proton moves eastward in the plane of Earth’s magnetic field so that the distance from the ground remains constant.

  What speed is the speed of the proton if Earth’s magnetic field points north and has a magnitude of 5.0 x 10-5 T?

Answer 1

Write out the mass and charge of a proton (these are well known experimentally)

Select a useful coordinate system. Set East as +x, North as +y, Up as +z.

The sum of the forces in the vertical are zero to keep the proton at a constant height.

The upward force is the magnetic force, and the downward force is the weight force.

The smallest angle between the velocity and magnetic field vector directions (theta) = 90 degrees. sin(90 deg) = 1.

Use algebra division to solve for v = (mg)/(qB).

Substitute in the values. This is a small speed, only a few milimeters per second.