Potential at a General Point Due to a Dipole

Q. Two positive charges $(+10\text{C})$ are kept on the arc of a circle and a negative charge $(-20\text{C})$ at the origin (centre of circle). Find the magnitude of net dipole moment for the given system.

1. $89.3\text{C-m}$
2. $59.3\text{C-m}$
3. $69.3\text{C-m}$
4. $79.3\text{C-m}$

Q. Three charges are arranged on the vertices of an equilateral triangle as shown in figure. Find the magnitude of dipole moment of the combination.

1. $\sqrt{2}qd$
2. $\sqrt{3}qd$
3. $\sqrt{5}qd$
4. $\sqrt{6}qd$

Q. A positive point charge $q$ is fixed at origin. A short dipole with a dipole moment $p$ is placed along the $x-$axis far away from the origin with $p$ pointing along the $+x-$axis. The kinetic energy of the dipole when it reaches distance $d$ from origin is

1. $\frac{3qp}{8\pi {ϵ}_0{d}^2}$
2. $\frac{qp}{4\pi {ϵ}_0{d}^2}$
3. $\frac{2qp}{4\pi {ϵ}_0{d}^2}$
4. $\frac{qp}{16\pi {ϵ}_0{d}^2}$

Q. Two short electric dipoles are placed as shown in figure.


The energy of electric interaction between these dipoles will be :

$[\text{Take}k=\frac{1}{4\pi {\epsilon }_0}]$

1. $$\frac{-2k{p}_1{p}_2\cos \theta }{r^3}$$
2. $$\frac{-4k{p}_1{p}_2\cos \theta }{r^3}$$
3. $$\frac{2k{p}_1{p}_2\cos \theta }{r^3}$$
4. $$\frac{-2k{p}_1{p}_2\sin \theta }{r^3}$$

Q. Find the magnitude of electric field due to a dipole at a point $\text{P}$ along the line joining point $\text{P}$ and centre of dipole as shown in figure.

1. $3.5\times {10}^{-3}\text{N/C}$
2. $2.0\times {10}^{-3}\text{N/C}$
3. $3.0\times {10}^{-3}\text{N/C}$
4. $2.5\times {10}^{-3}\text{N/C}$

Q. Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p . If P is a point at a distance r from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle $\theta$ with the axis of the dipole, then the potential at P is given by (r >> 2a) (Where p = 2qa)

1. $V=\frac{pcos\theta }{4\pi {ϵ}_0{r}^2}$
2. $V=\frac{pcos\theta }{4\pi {ϵ}_{0}r}$
3. $V=\frac{psin\theta }{4\pi {ϵ}_{0}r}$
4. $V=\frac{pcos\theta }{2\pi {ϵ}_0{r}^2}$

Q. In the given situation the work done in moving a charge of 5C from point A to point B is .

1. $10J$
2. $50J$
3. $Zero$
4. None of these

Q. Two equal charges q of opposite sign separated by a distance 2a constitute an electric dipole of dipole moment p . If P is a point at a distance r from the centre of the dipole and the line joining the centre of the dipole to this point makes an angle $\theta$ with the axis of the dipole, then the potential at P is given by (r >> 2a) (Where p = 2qa)

1. $V=\frac{pcos\theta }{4\pi {ϵ}_0{r}^2}$
2. $V=\frac{pcos\theta }{4\pi {ϵ}_{0}r}$
3. $V=\frac{psin\theta }{4\pi {ϵ}_{0}r}$
4. $V=\frac{pcos\theta }{2\pi {ϵ}_0{r}^2}$