Question

A beam of electrons enters a region in which there are electric and magnetic fields directed at right angles. It passes straight through without deviation. 

Consider this as if electrons are travelling from the left side towards the right. The electric fields are going from top towards bottom. The magnetic fields are going into the plane of the paper/diagram.

A second beam of electrons travelling twice as fast as the first is then directed along the same line.

How is this second beam deviated?

A. Downwards in the plane of the paper.

B. Upwards in the plane of the paper.

C. Out of the plane of the paper.

D. Into the plane of the paper.

Kindly, tell me what should be its answer and why, please.

Thank You.

Answer 1

As per the condition given in the question,

Case I

Electric and magnetic fields are perpendicular to each other, when the electron beam will enter into the magnetic field along x axis,

Then there is no deflection because,

$F_B=F_E$

$e vB=eE$

Hence, no deflection will show.

Case II

The direction of magnetic field now changed,

Hence net magnetic field $F_B=2e v\times B$ (Magnetic force will be in upward direction)

and electrostatic force $(F_E)=eE$ (in upward direction)

Hence net force will be in upward direction so the charge will move in upward direction. Hence correct answer is option B.