Torque on a Dipole

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

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

Q. The torque acting on a dipole of moment $\overrightarrow{P}$ in an electric field $\overrightarrow{E}$ is

1. $\overrightarrow{P}.\overrightarrow{E}$
2. $\overrightarrow{P}\times \overrightarrow{E}$
3. $Zero$
4. $\overrightarrow{E}\times \overrightarrow{P}$

Q. Two small dipoles of dipole moment $P_1$ and $P_2$ are placed as shown in figure. $k=\frac{1}{4\pi {ϵ}_o}$

1. Torque on $P_2$ due to $P_1$ is zero
2. Torque on $P_1$ due to $P_2$ is $\frac{2k{P}_1{P}_2}{r^3}$
3. Torque on $P_1$ due to $P_2$ is zero
4. Force on $P_1$ due to $P_2$ is zero

Q. A parallel plate capacitor with plate area A and initial separation d is connected to battery of EMF $V_0$. work done by external force to increase separation of plates from d to 2d slowly is
[Battery remains connected]

1. $\frac{{\epsilon }_{0}A{V}_0^2}{4d}$
2. $\frac{{\epsilon }_{0}A{V}_0^2}{d}$
3. $\frac{{\epsilon }_{0}A{V}_0^2}{2d}$
4. $\frac{{\epsilon }_{0}A{V}_0^2}{3d}$

Q. An electric dipole consisting of two opposite charges of $2\times {10}^{-6}C$ separated by a distance of 3cm is placed in an electric field of $2\times {10}^{5}N/C$. The maximum torque on the dipole will be

1. $12\times {10}^{–1}Nm$
2. $12\times {10}^{–3}Nm$
3. $24\times {10}^{–1}Nm$
4. $24\times {10}^{–3}Nm$

Q. A dipole with the magnitude of dipole moment 0.5 C-m is placed in an external uniform electric field of magnitude $10\frac{N}{C}$. $\overrightarrow{p}$ makes an angle of ${60}^{\circ }$ with $\overrightarrow{E}$. What is the potential energy of the dipole in the current configuration provided that the potential energy is taken zero when dipole is perpendicular to the applied field?

1. $-10J$
2. $-5J$
3. $zero$
4. $-2.5J$

Q. when a force F1 is applied on a wire its length is L1 & when a force F2 on the same wire its final length is L2. What is the initial length of the wire when no force is applied on it?

Q. An electrical dipole of dipole moment ${}^{\prime }{p}^{\prime }$ is placed in an electric field of intensity ${}^{\prime }{E}^{\prime }$. The dipole acquires a position such that the axis of the dipole makes an angle $\theta$ with electric field. Assuming that the potential energy of the dipole to be zero when $\theta ={90}^{\circ }$, the torque on dipole and the potential energy of the dipole will be respectively

1. $pE\sin \theta ,-pE\cos \theta$
2. $pE\cos \theta ,-pE\sin \theta$
3. $pE\sin \theta ,2pE\cos \theta$
4. $pE\sin \theta ,-2pE\cos \theta$