A point dipole vec{p} = -p_0hat{x} is kept at | vedclass

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(D) The potential $V$ at any point on the equatorial plane (the $y$-axis in this case) of a dipole is zero because the potential due to the positive a

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$0, \frac{-\vec{p}}{4\pi\varepsilon_0 d^3}$

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(D) The potential $V$ at any point on the equatorial plane (the $y$-axis in this case) of a dipole is zero because the potential due to the positive and negative charges of the dipole cancels out at every point on this plane.$V = 0$The electric field $\vec{E}$ at a point on the equatorial plane at a distance $d$ from the dipole is given by the formula:$\vec{E} = -\frac{1}{4\pi\varepsilon_0} \frac{\vec{p}}{d^3}$Substituting the given dipole moment $\vec{p} = -p_0\hat{x}$,the electric field is directed along the positive $x$-axis,which is consistent with the direction of $-\vec{p}$.Thus,the potential is $0$ and the electric field is $-\frac{\vec{p}}{4\pi\varepsilon_0 d^3}$.

$A$ point dipole $\vec{p} = -p_0\hat{x}$ is kept at the origin. The potential and electric field due to this dipole on the $y$-axis at a distance $d$ are,respectively: (Take $V = 0$ at infinity)

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