Question

An electron enters a region where magnetic and electric (E) fields are mutually perpendicular to one another, then
A. It will always move in the direction of B
B. It will always move in the direction of E
C. It always possess circular motion
D. It can go undeflected also

Answer 1

Hint: When a charged particle is moving in a region with an electric field, then it experiences the electric force in the direction parallel to the direction of the electric field. When a charged particle enters into the region with a magnetic field then it experiences magnetic force which is perpendicular to the motion, i.e. the deflection in the direction of the magnetic force.


Formula used:
\[\overrightarrow F = q\overrightarrow E + q\left( {\overrightarrow v \times \overrightarrow B } \right)\], here F is the net force acting on the particle of charge q moving with speed v in a region with magnetic field B and electric field E.


Complete answer:
It is given that an electron enters in a region where magnetic field and electric fields are mutually perpendicular to one another.
Using Lorentz’s law of force on a moving charged particle in a region of magnetic field and electric field, the total force acting on the particle is,
\[\vec F = q\vec E + q\left( {\vec v \times \vec B} \right)\]
So, the electric force component is \[{\vec F_e} = q\vec E\]acting along the direction of the electric field. If the initial velocity is in the direction making some angle with the electric field then it is not necessary that it always move in the direction of the electric field.
The magnetic field component is \[{\vec F_B} = q\left( {\vec v \times \vec B} \right)\]acting along the direction perpendicular to the magnetic field. Considering non-zero electric fields in the region, it is not necessary that the electron will always move in the direction of the magnetic field or have circular motion.
But when the magnitude of electric force and magnetic force is equal and acting in opposite direction, then the net force will be zero, i.e. the electron can move undeflected.
So, the most appropriate description of the motion of an electron is that it can also move undeflected.
Therefore, the correct option is (D).


Note:For undeflected motion of the electron, the orientation of the electric field and magnetic field be so that the net force acting on the electron is zero.