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(C) The given arrangement of charges is an electric dipole placed along the $z$-axis,with the positive charge at $(0, 0, a/2)$ and the negative charge

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zero

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(C) The given arrangement of charges is an electric dipole placed along the $z$-axis,with the positive charge at $(0, 0, a/2)$ and the negative charge at $(0, 0, -a/2)$.The electric potential $V$ at any point $(x, y, z)$ due to an electric dipole is given by $V = \frac{1}{4\pi\epsilon_0} \frac{\vec{p} \cdot \vec{r}}{r^3}$.For a dipole centered at the origin,the equatorial plane is the $xy$-plane $(z = 0)$.At any point on the $xy$-plane,the distance from the positive charge is equal to the distance from the negative charge,so the potential $V$ is zero everywhere on the $xy$-plane.The initial position is $(-a, 0, 0)$,which lies on the $xy$-plane,so $V_i = 0$.The final position is $(0, a, 0)$,which also lies on the $xy$-plane,so $V_f = 0$.The work done by the electric field $W_e$ is given by $W_e = -\Delta U = -q_0(V_f - V_i)$,where $q_0$ is the test charge.Since $V_f = V_i = 0$,the work done $W_e = -q_0(0 - 0) = 0$.

Positive and negative point charges of equal magnitude are kept at $(0, 0, a/2)$ and $(0, 0, -a/2)$,respectively. The work done by the electric field when another positive point charge is moved from $(-a, 0, 0)$ to $(0, a, 0)$ is

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