Question

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected in the region such that its velocity is pointed along the direction of fields, then the electron
A. Speed will decrease
B. Speed will increase
C. Will turn towards left of direction of motion
D. Will turn towards right of direction of motion

Answer 1

Hint: Both electric and magnetic fields will be acting on the electron particle. So, by using the formula to find the force acting on the electron due to the fields, we can determine the state of the electron after entering the field.

Formula used:
Force due to magnetic field, $\vec{F}_{B}=-e(\vec{v}\times \vec{B})$ where, e is the electron charge, v is its velocity and B is the magnetic field strength.
Force due to electric field, $\vec{F}_{E}=-e\vec{E}$ where e is the charge on electrons and E is the electric field.

Complete step-by-step answer:
We have been given that the direction of both magnetic and electric fields is the same and the velocity vector of the electron is also pointed in the direction of both the fields.
So, force on the electron due to the electric field, $\vec{F}_{E}=-e\vec{E}$ ………. (i)
where e is the charge on an electron and E is the electric field.
And force on the electron due to the magnetic field, $\vec{F}_{B}=-e(\vec{v}\times \vec{B})$ where, e is the electron charge, v is its velocity and B is the magnetic field strength.
As the direction of velocity vector of the electron and that of the magnetic field is the same, the angle between the vectors will be zero.
Therefore, $\vec{F}_{B}=-e(\vec{v}\times \vec{B})=0$ ……….(ii)
From (i) and (ii), net force acting on the electron, $\vec{F}=\vec{F}_{E}+\vec{F}_{B}=-e\vec{E}$
Thus, net force on the electron is opposite to its direction of motion and will therefore reduce its speed.
Hence, option a is the correct answer.

Note: The direction of the motion and the fields are the main key here. The particle would have changed its direction, in case there was some angle between its velocity vector and field vector. Since, this is an electron, the charge on it is negative and hence the electric force is also negative and has it been a proton, the force would have also been in the same direction as of its motion.