Potential Energy of a Dipole in Uniform Electric Field

Q. An electric dipole of moment p is placed in the position of stable equilibrium in uniform electric field of intensity E. If it is rotated through an angle $\theta$ from the initial position, the potential energy of electric dipole in the final position is

1. $pEcos\theta$
2. $pEsin\theta$
3. $pE(1-cos\theta )$
4. $-pEcos\theta$

Q. An electric dipole of moment $\overrightarrow{p}$ is placed normal to the lines of force of electric intensity $\overrightarrow{E}$, then the work done in rotating it through an angle of ${180}^{\circ }$ is

1. pE
2. +2pE
3. -2pE
4. Zero

Q.

An Electric field $\overrightarrow{E}=3\hat{i}-5\hat{j}+\hat{k}$ exists in space. Find the potential difference between $(1,2,1)$ and $(4,3,5)$.

1. $4\text{V}$
2. $-18\text{V}$
3. $6\text{V}$
4. $-8\text{V}$

Q. A dipole of moment $\overrightarrow{p}$ is placed normal to an electric field $\overrightarrow{E}$. Work done in rotating it by an angle of $\pi$ is .

1. pE
2. +2pE
3. -2pE
4. $zero$

Q. A dipole of moment $\overrightarrow{p}$ is placed normal to an electric field $\overrightarrow{E}$. Work done in rotating it by an angle of $\pi$ is .

1. pE
2. +2pE
3. -2pE
4. $zero$

Q. Find the minimum work done to form a solid sphere of radius $R$ and total charge $Q$.
[Assume all the charges are at infinity initially]

1. $\frac{3}{5}\frac{K{Q}^2}{R}$
2. zero
3. $\frac{2}{5}\frac{K{Q}^2}{R}$
4. $\frac{6}{5}\frac{K{Q}^2}{R}$