Potential Energy of a Dipole in Uniform Electric Field

Q. A charge $Q$ is placed at a perpendicular distance $\frac{a}{2}$ above the centre of the horizontal, square surface of edge length $a$ as shown in figure. Find the flux of the electric field through the square surface.

1. $\frac{Q}{3{\epsilon }_0}$
2. $\frac{Q}{2{\epsilon }_0}$
3. $\frac{Q}{{\epsilon }_0}$
4. $\frac{Q}{6{\epsilon }_0}$

Q. Two point charges of $3.2\times {10}^{-19}C$ and $-3.2\times {10}^{-19}C$ are separated from each other by $2.4\times {10}^{-10}m$.The dipole is situated in a uniform electric field of intensity $4\times {10}^{5}V{m}^{-1}.$ If the work done in rotating the dipole by ${180}^{\circ }$ is $n\times {10}^{-23}J$, the value of $n$ is . (Write upto two decimal places)

Q. An electric dipole of moment p is placed in the position of stable equilibrium in uniform electric field of intensity E. If it is rotated through an angle $\theta$ from the initial position, the potential energy of electric dipole in the final position is

1. $pEcos\theta$
2. $pEsin\theta$
3. $pE(1-cos\theta )$
4. $-pEcos\theta$

Q. An electric dipole of moment p is placed in the position of stable equilibrium in uniform electric field of intensity E. If it is rotated through an angle $\theta$ from the initial position, the potential energy of electric dipole in the final position is

1. $pEcos\theta$
2. $pEsin\theta$
3. $pE(1-cos\theta )$
4. $-pEcos\theta$

Q. An electric dipole of moment $\overrightarrow{p}$ is placed normal to the lines of force of electric intensity $\overrightarrow{E}$, then the work done in rotating it through an angle of ${180}^{\circ }$ is

1. pE
2. +2pE
3. -2pE
4. Zero

Q. A dipole of moment $\overrightarrow{p}$ is placed normal to an electric field $\overrightarrow{E}$. Work done in rotating it by an angle of $\pi$ is .

1. pE
2. +2pE
3. -2pE
4. $zero$

Q. A dipole with dipole moment $3.60nC-m$ is oriented at ${60}^{\circ }$ to an electric field of magnitude $4\times {10}^{9}N/C$, how much work is required to rotate the dipole until it is antiparallel to field.

1. $21.6J$
2. $3.6J$
3. $14.4J$
4. $7.2J$

Q. A charge $Q$ is placed at a perpendicular distance $\frac{a}{2}$ above the centre of the horizontal, square surface of edge length $a$ as shown in figure. Find the flux of the electric field through the square surface.

1. $\frac{Q}{{\epsilon }_0}$
2. $\frac{Q}{6{\epsilon }_0}$
3. $\frac{Q}{2{\epsilon }_0}$
4. $\frac{Q}{3{\epsilon }_0}$

Q. An electric dipole of dipole moment $p$ is placed in a uniform electric field $E$ in stable equilibrium position. Its moment of inertia about the centroidal axis is $I$. If it is displaced slightly from its mean position, find the period of small oscillations.

1. $2\pi \sqrt{\frac{pE}{I}}$
2. $2\pi \sqrt{\frac{I}{pE}}$
3. $\pi \sqrt{\frac{pE}{I}}$
4. $\pi \sqrt{\frac{I}{pE}}$

Q. A dipole with dipole moment $3.60nC-m$ is oriented at ${60}^{\circ }$ to an electric field of magnitude $4\times {10}^{9}N/C$, how much work is required to rotate the dipole until it is antiparallel to field.

1. $21.6J$
2. $3.6J$
3. $14.4J$
4. $7.2J$

Q. A dipole with dipole moment $3.60nC-m$ is oriented at ${60}^{\circ }$ to an electric field of magnitude $4\times {10}^{9}N/C$, how much work is required to rotate the dipole until it is antiparallel to field.

1. $21.6J$
2. $3.6J$
3. $14.4J$
4. $7.2J$