Question

Two identical positive charges are placed near each other. At the point halfway between the two charges,

(a) the electric field is zero and the potential is positive.

(b) the electric field is zero and the potential is zero.

(c) the electric field is not zero and the potential is positive.

(d) the electric field is not zero and the potential is zero.

(e) None of these statements is true.

Short answer

The correct answer is option (a) the electric field is zero and the potential is positive.

Step-by-step solution

Understanding electric field

The electric field at a particular point halfway among the two positive charges is the sum of the electric fields from each positive charge.

Evaluation of the electric field and electric potential

The electric field at any point due to a point charge is given by,

\(\overrightarrow E = \frac{{kQ}}{{{r^2}}}\hat r\)

Here, k is the Coulomb’s constant, Q is the charge and r is the distance.

The electric field is a vector quantity. At the midpoint between the two charges, the magnitude of the electric field is the same but opposite in direction. Therefore, due to both charges, the electric field is added up to give zero at the midpoint.

The electric potential is given as:

\(V = \frac{{kQ}}{r}\)

Electric potential is a scalar quantity. The electric potential due to a positive point charge is positive. So, the electric potential due to both the charges will add up to give a positive value of the electric potential at the point halfway between the two charges.

Thus, the correct option is (a).