Electric Field Due to a Dipole at a General Point in Space

Q. The Gaussian surface for calculating the electric field due to a charge distribution is :

1. Any closed surface around the charge distribution.
2. A cylindrical surface.
3. A spherical surface.
4. A closed surface at every point of which electric field has a normal component which is zero or a fixed value.

Q. The magnitude of the electric field at a distance $r$ far away along the axis from an electric dipole is $E$. Find the magnitude of the electric field at distance $2r$ along the perpendicular bisector of the dipole.

1. $E/16$
2. $E/12$
3. $E/8$
4. $E/10$

Q. A point dipole of dipole moment $p$ is placed along $y$-axis, a point charge is placed at $x$-axis at distance $r$ from point dipole, find net force on dipole due to point charge.

1. $\frac{2kp}{r^3}{q}_0\hat{j}$
2. $\frac{kp}{r^3}{q}_0\hat{j}$
3. $\frac{kp}{r^3}{q}_0\hat{j}$
4. zero because total charge on dipole is zero.

Q. A hollow sphere contains a dipole with dipole moment $10\text{C-m}$ and each charge having a magnitude of $100\text{C}$. The net flux crossing through the surface of the shell is?

1. $\frac{100}{{\epsilon }_0}$
2. $\frac{200}{{\epsilon }_0}$
3. Zero
4. Data Insufficient

Q. An electric dipole is placed at an angle of ${30}^{\circ }$ with an electric field intensity $2\times {10}^5\text{N/C}$. It experiences a torque equal to $4\text{Nm}$. The charge on the dipole, if the dipole length is $2\text{cm}$ is:

1. $5\text{mC}$
2. $2\text{mC}$
3. $7\mu C$
4. $8\text{mC}$

Q. The electric field due to a dipole at a distance r on its axis is

1. Directly proportional to $r^3$
2. Inversely proportional to $r^3$
3. Directly proportional to $r^2$
4. Inversely proportional to $r^2$

Q. A dipole is placed at the centre of a non-conducting spherical shell of radius $r$. If the shell is uniformly charged by a surface charge density $\sigma$, then the interaction energy of dipole and the shell is
(The dipole moment is $p$)

1. zero
2. $\frac{p\sigma }{{ϵ}_{0}r}$
3. $\frac{p\sigma }{4{ϵ}_0}$
4. $\frac{p\sigma }{{ϵ}_0{r}^2}$

Q. A hollow sphere contains a dipole with dipole moment $10\text{C-m}$ and each charge having a magnitude of $100\text{C}$. The net flux crossing through the surface of the shell is?

1. $\frac{100}{{\epsilon }_0}$
2. $\frac{200}{{\epsilon }_0}$
3. Zero
4. Data Insufficient

Q. The distance between the two charges +q and -q of a dipole is r. On the axial line at a distance d from the centre of dipole, the intensity is proportional to

1. $\frac{q}{d^2}$
2. $\frac{qr}{d^2}$
3. $\frac{q}{d^3}$
4. $\frac{qr}{d^3}$