Geomagnetic Exercise without numbers

Question

At the equator, there is a magnetic field B horizontal to the North and magnitude B: ... T (given)

What is the magnitude and direction of the velocity of an electron e (m_e =9.31 x 10^-31 Kg and q_e = -1.6 x10^-19 c) in a way that its weight is in balance with the force exerted on it.

We need the geographical direction of V. (N, S, W or E).

Please can you tell me how do we solve such a problem?

Answer 1

The magnetic force on the moving electron is

 

F = -ev x B

 

This must balance the downward vertical weight mg of the electron.  This requires that -ev x B point vertically up, which implies that v x B points vertically down.  Given that B points N, v must point W so that v x B points down.  Since the directions of B and v are perpendicular, we can easily find the magnitude of v from

 

evB = mg

 

v = mg / (eB)

 

Do you follow the reasoning?