Question

A beam of electrons passes undeflected through mutually perpendicular electric and magnetic fields. If the electric field is switched off and the same magnetic field is maintained, the electrons move.
A. In an elliptical orbit
B. In a circular orbit
C. Along a parabolic path
D. Along a straight line

Answer 1

Electron beam passes through electric field E from left to right and E is directed vertically downwards. The electrostatic force is directed upwards, The velocity of electrons moving inwards when the magnetic field is applied perpendicular to the electrical field.

Complete step by step solution:
The condition of electrons that should pass undeflected through the cross fields is given below,
That is the velocity of the electrons is,
$V = \dfrac{E}{B}$
Here, $E$ is the electric field
$B$ is the magnetic field.
If we are off the electric field then there will be only the magnetic field as the only force that is present. Generally, the velocity has the two components they are along the $B$ and the normal to the $B$
The perpendicular components effect only we can see due to the movement of electrons which is in a circular motion. The electrons travel along direction B because of the horizontal components.
In the $2D$ module, the visualization is confined, after combining these two we can develop the $3D$ module. Hence the circular and rectilinear motions are occurring frequently. The radius of the helix is constant because the velocity is constant.
So, the answer is option (B).

Note:
If the electron is un deviated then we have both electric and magnetic fields that are perpendicular to each other.
If the magnetic field is absent the electric field is parallel to the beam hence the electron's speed gets increased in the same direction where the electron is un deviated.
If both electric and magnetic fields are present which is parallel to the beam here also electron deviates hence the speed of the electrons change