Four-point +ve charges of the same magnitude (Q) are placed at four corners of a rigid square frame as shown in the figure. The plane of the frame is perpendicular to Z-axis. If a –ve point charge is placed at a distance z away from the above frame (z<<L) then
– ve charge oscillates along the Z-axis.
It moves away from the frame.
It moves slowly towards the frame and stays in the plane of the frame.
It passes through the frame only once.
The four positive charges at the corners of the square produce a net electric field along the Z-axis directed away from the center of the square (due to symmetry, horizontal components cancel) . A negative charge placed on the Z-axis experiences an attractive force towards the center of the square () .
For small displacements (where ), the restoring force is approximately proportional to the displacement (), which is the condition for Simple Harmonic Motion (SHM) . Therefore, the negative charge will oscillate back and forth along the Z-axis about the center of the frame.
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