A dipole consisting of two charges pm q separ | vedclass

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(D) The potential at any point on the surface of a grounded conducting sphere is always zero $(V = 0)$.The total induced charge $q_{	ext{induced}}$ o

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(D) The potential at any point on the surface of a grounded conducting sphere is always zero $(V = 0)$.The total induced charge $q_{	ext{induced}}$ on a grounded sphere due to an external charge distribution can be found using the method of images or by considering the potential at the center of the sphere.For a dipole placed at a distance $D$ from the center of the sphere,the potential at the center of the sphere due to the dipole is given by $V = \frac{1}{4\pi\epsilon_0} \frac{\vec{p} \cdot \vec{r}}{r^3}$.Since the dipole moment vector $\vec{p}$ is perpendicular to the line joining the center of the dipole and the center of the sphere (the position vector $\vec{r}$),the dot product $\vec{p} \cdot \vec{r} = 0$.Therefore,the potential at the center of the sphere due to the dipole is zero. Since the sphere is grounded,the total induced charge on the sphere must be zero to maintain the potential at zero.

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