Question

A positive test charge is released from rest in a uniform electric field. Which of the following best describes its initial motion?
A. It will move with constant velocity along an equipotential line
B. It will move with constant acceleration along an equipotential line
C. It will move with constant acceleration along an electric field line
D. It will move with constant velocity along an electric field line

Answer 1

When we released a test charge in the uniform electric field, the only force that acts on the charge is the electric force. Recall the expression for the electric force and identify the direction of the force on the positive test charge. Use Newton’s second law to determine the nature of acceleration of the test charge.

Complete answer:
When we released a test charge in the uniform electric field, the only force that acts on the charge is the electric force given by the expression,
${\vec F_e} = q\vec E$
Here, q is the charge and E is the electric field.
From the above equation, we can clearly see that the force acting on the charge is along the direction of the electric field. Therefore, the charge will move along the direction of the electric field since it is the positive charge.

Now, we can determine the acceleration of the test charge using Newton’s second law as follows,
$F = ma = qE$
$\Rightarrow a = \dfrac{{qE}}{m}$
Here, m is the mass of the charge.

The quantities q and m are constant and also the electric field is uniform that means it does not change. Therefore, the acceleration of the charge will be constant. Thus, the correct answer is option C.

We know that the equipotential line is the region where the electric potential remains constant. The electric potential remains constant in the region perpendicular to the direction of electric field. But the charges always move along the electric field. Therefore, options A and B are incorrect. The constant velocity implies that the acceleration of the charge is zero. But we have seen that the charge moves with constant acceleration. Therefore, the option D is incorrect.

So, the only correct answer is option C.

Note: The direction of the electric field can be opposite to the electric field when the charge is negative. This is because the positive charge is attracted towards the lower potential that is along the electric field and the negative charge is attracted towards the higher potential that is opposite to the direction of the electric field. Students must know the meaning of equipotential surface. If we place a test charge at the centre of the sphere, the potential due to this charge every point of the surface of the sphere will be the same.