Torque on a Dipole

Q. An electric dipole consisting of two opposite charges of $2\times {10}^{-6}C$ each, separated by a distance of 3 cm 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. Two small identical dipoles $\text{AB}$ and $\text{CD}$, each having dipole moment of magnitude $p$ are kept at an angle of ${120}^{\circ }$ as shown in the figure. If this system is subjected to an uniform electric field of magnitude $E$ directed along $+x$ direction, then the magnitude of torque acting on this is

1. $\frac{pE}{2}$
2. $\frac{pE}{4}$
3. $2pE$
4. $pE$

Q. An electric dipole of dipole moment $\overrightarrow{p}=(2.0\hat{i}+3.0\hat{j})\mu \text{C-m}$ is placed in a uniform electric field $\overrightarrow{E}=(3.0\hat{i}+2.0\hat{k})\times {10}^5\text{N/C}$

1. The potential energy of the dipole is $+0.6\text{J}$
2. The torque that $\overrightarrow{E}$ exertes on $\overrightarrow{p}$ is $(0.6\hat{i}-0.4\hat{j}-0.9\hat{k})\text{N-m}$
3. The potential energy of the dipole is $-0.6\text{J}$
4. If the dipole is rotated in the electric field , the maximum potential energy of the dipole is $1.3\text{J}$

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 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. 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. An electric dipole consisting of two opposite charges of $2\times {10}^{-6}C$ each, separated by a distance of 3 cm 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. An electric dipole has a fixed dipole moment $\overrightarrow{p}$, which makes angle $\theta$ with respect to $x-$ axis. When system is subjected to an electric field $\overrightarrow{E_1}=E\hat{i},$ it experiences a torque $\overrightarrow{{\tau }_1}=-\tau \hat{k}$. When subjected to another electric field $\overrightarrow{E_2}=\sqrt{3}E\hat{j}$, it experiences a torque $\overrightarrow{{\tau }_2}=-\overrightarrow{{\tau }_1}$. The angle $\theta$ is

1. ${90}^{\circ }$
2. ${30}^{\circ }$
3. ${60}^{\circ }$
4. ${45}^{\circ }$

Q. A point particle of mass $M$ is attached to one end of a massless rigid non-conducting rod of length $L$. Another point particle of same mass is attached to the other end of the rod. The two particles carry charges $+q$ and $-q$ repectively. This arrangement is held in a region of uniform electric field $E$ such that the rod makes a small angle $(\theta <5^{\circ })$ with the field direction. The minimum time needed for the rod to become parallel to the field after it is set free. (rod rotates about centre of mass)

1. $2\pi \sqrt{\frac{ML}{2qE}}$
2. $\pi \sqrt{\frac{ML}{2qE}}$
3. $\frac{\pi }{2}\sqrt{\frac{ML}{2qE}}$
4. $4\pi \sqrt{\frac{ML}{2qE}}$

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. An electric dipole has a fixed dipole moment $\overrightarrow{p}$, which makes angle $\theta$ with respect to $x-$ axis. When system is subjected to an electric field $\overrightarrow{E_1}=\sqrt{3}E\hat{i},$ it experiences a torque $\overrightarrow{{\tau }_1}=-\tau \hat{k}$. When subjected to another electric field $\overrightarrow{E_2}=E\hat{j}$, it experiences a torque $\overrightarrow{{\tau }_2}=-\overrightarrow{{\tau }_1}$. The angle $\theta$ is

1. ${90}^{\circ }$
   
2. ${60}^{\circ }$
   
3. ${45}^{\circ }$
   
4. ${30}^{\circ }$
   

Q. An electric dipole is placed at an angle ${30}^{\circ }$ with an electric field intensity $2\times {10}^{5}N{C}^{-1}$. It experiences a torque equal to $4Nm$. The charge on the dipole(in $mC$), if the dipole length is $2cm$, is

Q. An electric dipole is placed at an angle ${30}^{\circ }$ with an electric field intensity $2\times {10}^{5}N{C}^{-1}$. It experiences a torque equal to $4Nm$. The charge on the dipole(in $mC$), if the dipole length is $2cm$, is

Q. An electric dipole is situated in an electric field of uniform intensity E whose dipole moment is p and moment of inertia is I. If the dipole is displaced slightly from the equilibrium position, then the angular frequency of its oscillations is

1. ${\left(\frac{pE}{I}\right)}^{1/2}$
2. ${\left(\frac{pE}{I}\right)}^{3/2}$
3. ${\left(\frac{I}{pE}\right)}^{1/2}$
4. ${\left(\frac{p}{IE}\right)}^{1/2}$

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. The force with which the plates of a parallel plate capacitor, having charge Q and area of each plate A, attract each other is

1. zero
2. $\frac{Q^2}{{\epsilon }_{0}A}$
3. $\frac{Q^2}{\sqrt{2}{\epsilon }_{0}A}$
   
4. $\frac{Q^2}{2{\epsilon }_{0}A}$

Q. A point particle of mass $M$ is attached to one end of a massless rigid non-conducting rod of length $L$. Another point particle of same mass is attached to the other end of the rod. The two particles carry charges $+q$ and $-q$ repectively. This arrangement is held in a region of uniform electric field $E$ such that the rod makes a small angle $(\theta <5^{\circ })$ with the field direction. The minimum time needed for the rod to become parallel to the field after it is set free. (rod rotates about centre of mass)

1. $2\pi \sqrt{\frac{ML}{2qE}}$
2. $\pi \sqrt{\frac{ML}{2qE}}$
3. $\frac{\pi }{2}\sqrt{\frac{ML}{2qE}}$
4. $4\pi \sqrt{\frac{ML}{2qE}}$

Q.

Two equal and opposite charges of $4\times {10}^{-8}$ C when placed $2\times {10}^{-2}cm$ away, form a dipole. If this dipole is placed in an external electric field of $4\times {10}^8$ newton/coulomb, the value of maximum torque and the work done in rotating it through ${180}^{\circ }$ will be

1. $64\times {10}^{-4}Nmand64\times {10}^{-4}J$
2. $32\times {10}^{-4}Nmand32\times {10}^{-4}J$
3. $64\times {10}^{-4}Nmand32\times {10}^{-4}J$
4. $32\times {10}^{-4}Nmand64\times {10}^{-4}J$