$8$Electrostatics deals with the study of forces, fields and potentials arising from static charges. Force and electric field, due to a point charge is basically determined by Coulomb's law. For symmetric charge configurations, Gauss's law, which is also based on Coulomb's law, helps us to find the electric field. A charge/a system of charges like a dipole experience a force/torque in an electric field. Work is required to be done to provide a specific orientation to a dipole with respect to an electric field. Answer the following questions based on the above : (a) Consider a uniformly charged thin conducting shell of radius R. Plot a graph showing the variation of $\displaystyle |\vec{\mathrm{E}}|$ with distance $\displaystyle \mathrm{r}$ from the centre, for points $\displaystyle 0 \leq \mathrm{r} \leq 3 \mathrm{R}$. (b) The figure shows the variation of potential V with $\displaystyle \frac{1}{\mathrm{r}}$ for two point charges $\displaystyle \mathrm{Q}_{1}$ and $\displaystyle \mathrm{Q}_{2}$, where V is the potential at a distance r due to a point charge. Find $\displaystyle \frac{\mathrm{Q}_{1}}{\mathrm{Q}_{2}}$. 2023_CBSE_Physics_Set_Region4_Subset_Set1_Q34_SECTION-E_b_p13_19

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(c) An electric dipole of dipole moment of $\displaystyle 6 \times 10^{-7} \mathrm{C}-\mathrm{m}$ is kept in a uniform electric field of $\displaystyle 10^{4} \mathrm{~N} / \mathrm{C}$ such that the dipole moment and the electric field are parallel. Calculate the potential energy of the dipole.

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(c) An electric dipole of dipole moment $\displaystyle \overrightarrow{\mathrm{p}}$ is initially kept in a uniform electric field $\displaystyle \overrightarrow{\mathrm{E}}$ such that $\displaystyle \overrightarrow{\mathrm{p}}$ is perpendicular to $\displaystyle \overrightarrow{\mathrm{E}}$. Find the amount of work done in rotating the dipole to a position at which $\displaystyle \overrightarrow{\mathrm{p}}$ becomes antiparallel to $\displaystyle \overrightarrow{\mathrm{E}}$.

Physics · Electric Charges and Fields