Question

Consider an electron near the Earth's equator. In which direction does it tend to deflect if its velocity is (a) directed downward?

Answer 1

The electron near the Earth's equator doesn't deflect if it's velocity is directed downwards.

Assume that north is directed along upwards, south is directed along downwards, east is directed along rightwards, and west is directed along leftwards.

The magnetic force on the charge q, moving with velocity v in the magnetic field B is given by

F=q(→v×→B)=qvBsinθ ..(1)

Here,

θ is the angle between the magnetic field and velocity.

Inside the Earth, the Earth's magnetic field is along northward (upwards), and the velocity is given to be along southwards (downwards) making an angle of 180°. In equation (1) sin180°=0. So, no magnetic force acts on the electron

Therefore,

The electron didn't deflect if it is directed downwards.

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