Question

An electron moving in the direction of the +x-axis enters a region where both an electric and magnetic field are applied. The electron moves through the two fields undeflected (with constant velocity). If the magnetic field is in the -y direction, what is the direction of the electric field in this region?

Answer 1

The direction of the electric field will be along z-direction.

Step-by-step explanation:

When electrons enter in a region where there is only magnetic field, then force exerted by the magnetic field will be

`\vec{F_(B)} = e(\vec{v} * \vec{B})`

This force will deflect the electron in a direction perpendicular to its motion and also perpendicular to the magnetic field.

Whereas in the presence of electric field, force exerted by the electric field is

`\vec{F_(E)} = e\vec{E}`

The direction is opposite to the direction of electric field.

As a result, electron deflected by magnetic field is nullified by the deflection by electric field. As a result, electron moves undeflected.

So, if the direction of the magnetic field is along y-direction, the direction of the electric field has to along z-direction.