| 1. | \(9~{\mu \text{F}}\) | 2. | \(2~{\mu \text{F}}\) |
| 3. | \(3~{\mu \text{F}}\) | 4. | \(6~{\mu \text{F}}\) |
| 1. | \(\left(\dfrac{8}{3}\right)qk\) | 2. | \(\left(\dfrac{3}{8}\right)qk \) |
| 3. | \(\left(\dfrac{5}{8}\right)qk\) | 4. | \(\left(\dfrac{8}{5}\right)qk\) |
| 1. | \(\dfrac{rV}{R^2}\) | 2. | \(\dfrac{R^2V}{r^3}\) |
| 3. | \(\dfrac{RV}{r^2}\) | 4. | \(\dfrac{V}{r}\) |
An electric dipole of moment \(p\) is placed in a uniform electric field \(E\) such that the dipole axis is initially perpendicular to the direction of the electric field. The dipole is then slowly rotated in the field until it has turned through a total angle of \(180^\circ.\) What is the total work done by the external agent in rotating the dipole?
1. \(pE\)
2. \(pE/2\)
3. \(2pE\)
4. zero
Identify the incorrect statement from the following:
| 1. | The equipotential surface created by a single-point charge is spherical. |
| 2. | Equipotential surfaces can also be constructed for a dipole. |
| 3. | Equipotential surfaces are always perpendicular to electric field lines. |
| 4. | The work done in moving a test charge along an equipotential surface is positive. |
| 1. | zero | 2. | \(\dfrac{-q^2}{4\pi\varepsilon_0d}\) |
| 3. | \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(3-\dfrac{1}{\sqrt2}\Big)\) | 4. | \(\dfrac{-q^2}{4\pi\varepsilon_0d}\Big(6-\dfrac{1}{\sqrt2}\Big)\) |

| 1. | \(3~\text{V/m},\) directed along the positive \(x\text-\)axis |
| 2. | \(3~\text{V/m},\) directed along the negative \(x\text-\)axis |
| 3. | \(6~\text{V/m},\) directed along the positive \(x\text-\)axis |
| 4. | \(6~\text{V/m},\) directed along the negative \(x\text-\)axis |