Four point positive charges of same magnitude | vedclass

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

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Negative charge oscillates along the $z$-axis.

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(A) The four positive charges $Q$ at the corners of the square create an electric field along the $z$-axis directed towards the origin (the center of the square). For a negative charge $-q$ placed at a small distance $z$ from the center along the $z$-axis,the net electrostatic force is directed towards the center of the square. The force is given by $F = -k z$,where $k$ is a positive constant. Since the force is proportional to the displacement $z$ and directed towards the equilibrium position (the origin),the negative charge will execute simple harmonic motion $(SHM)$ about the origin along the $z$-axis. Therefore,the negative charge oscillates along the $z$-axis.

Four point positive charges of same magnitude $Q$ are placed at four corners of a rigid square frame in $xy$ plane as shown in the figure. The plane of the frame is perpendicular to the $z$-axis. If a negative point charge is placed at a distance $z$ away from the above frame $(z << L)$,then:

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