Question

Acceleration of a charged particle of charge ‘q’ and mass ‘m’ moving in a uniform electric field of strength ‘E’.
A) $\dfrac{{qE}}{m}$.
B) $\dfrac{m}{{qE}}$
C) $mqE$
D) $\dfrac{q}{{mE}}$

Answer 1

Hint:A charged particle under the influence of an electric field experiences an electrostatic force acting on the charged particle. The right hand rule can be used to find the direction of motion of the charged particle under the influence of the electric field.

Formula used:The formula of the force is given by $F = m \cdot a$ where F is the force m is the mass and a is the acceleration of the body. The force on the charge is equal to $F = q \cdot E$ where F is the force E is the electric field and q is the charged particle.

Complete step by step answer:
It is given that a charged particle is placed in the electric field and it starts moving due to the force experienced under the electric field. The force experienced under the electric field is given by,
$ \Rightarrow F = q \cdot E$………eq. (1)
Where F is the electrostatic force E is the electric field and q is the charge of the particle.
We know that a moving body with constant acceleration of mass m can be expressed in terms of force F as,
$ \Rightarrow F = m \cdot a$………eq. (2)
Where F is the force m is the mass and a is the acceleration of the body.
Equating the equation (1) and equation (2) we get,
$ \Rightarrow m \cdot a = q \cdot E$
$ \Rightarrow a = \dfrac{{q \cdot E}}{m}$
The acceleration ‘a’ of the particle of mass ‘m’ and charge ‘q’ in the electric field ‘E’ is given by$a = \dfrac{{q \cdot E}}{m}$.

The correct option for this problem is option A.

Note:The charge particle will always feel electrostatic force under the influence of the electric field and the charge of the particle i.e. positive or negative will decide the direction of the motion of the particle with charge ‘q’.