Four point positive charges of same magnitude | vedclass

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Question

(A) The four positive charges $(Q)$ at the corners of the square create an electric field directed towards the center of the square along the $Z$-axis

Vedclass · Accepted Answer

The negative charge oscillates along the $Z$-axis.

Vedclass · Answer

(A) The four positive charges $(Q)$ at the corners of the square create an electric field directed towards the center of the square along the $Z$-axis. For a negative charge $(-q)$ placed at a small distance $z$ on the $Z$-axis, the net electrostatic force exerted by the four charges will be directed towards the center of the square frame. The magnitude of this force is proportional to the displacement $z$ for small $z$ (i.e., $F \propto -z$). This acts as a restoring force. As the negative charge is attracted towards the center, it accelerates. When it reaches the center (the plane of the frame), the net force is zero, but due to its acquired velocity (inertia), it crosses the center and moves to the other side. The restoring force then acts in the opposite direction, slowing it down until it stops and is pulled back again. Thus, the negative charge performs simple harmonic motion (oscillates) along the $Z$-axis about the center of the frame.

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