Question

A high energy electron heads towards Washington DC from deep space. In which direction is the electron's initial deflection due to the Earth's magnetic field?

a. Atlantic ocean b. California c. Maine d. Florida

Suppose the electron is trapped by the Earth's magnetic field (on the side of the Earth away from the sun) in a circular orbit at a distance of 5 Earth radii from the Earth, estimate the size of its orbit assuming it is traveling at 1/10th the speed of light indicating your assumptions including the distance behavior of the Earth's B-field

What is the frequency of its orbit?

Answer 1

As the direction of earths magentic field is from pointing towards north. And electron with charge -e is travelling from perpendicular direction, the force on electron will be:

using right hand rule, v x B is towards east, but -e makes it towards west.

Hence, electron will tend to move towards west, and from Washington DC, west is California.

hence, the answer is (b) California.

At a height of 5 earth radius, i.e. 32000 km, we have value of magnetic field as:

B = 219 nT

as found from Internet.

Speed of electron v = c/10 = 3 x 10⁷ m/s

Hence, the radius of orbit is given by:

or

and frequency of orbit is:

or 35.50 kHz