question_answer

Assertion             :       If a point charge q is placed in front of an infinite grounded conducting plane surface, the point charge will experience a force.             Reason     :   This force is due to the induced charge on the conducting surface which is at zero potential.

A)             If both assertion and reason are true and the reason is the correct explanation of the assertion.

B)             If both assertion and reason are true but reason is not the correct explanation of the assertion.

C)             If assertion is true but reason is false.

D)             If the assertion and reason both are false.

E)                 If assertion is false but reason is true.

Correct Answer: A

Solution :

            This is the concept of electric image. If we are asked to find the force between an infinite earthed conductor and a point charge q placed at perpendicular distance l from the earthed conductor (see figure), than we proceed as follows. Firstly, the conductor being earthed implies V = 0. So, we redraw the situation in which we replace the conductor and introduce an IMAGE charge ­-q as shown. The force between the two charges (object charge q and image charge ?q) is the electrostatic force between the infinite grounded conductor and q. So,\[F=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}^{2}}}{{{(2l)}^{2}}}\]Þ\[F=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}^{2}}}{4{{l}^{2}}}\](attractive in nature)