Q 1 :    

The electrostatic potential due to an electric dipole at a distance 'r' varies as                            [2024]

• $r$

   

• $\frac{1}{r^2}$

   

• $\frac{1}{r^3}$

   

• $\frac{1}{r}$

   

Q 2 :    

The distance between charges +q and −q is $2\lambda$ and between +2q and −2q is $4\lambda$. The electrostatic potential at point P at a distance $r$ from center O is $-\alpha \left[\frac{{\displaystyle ql}}{{\displaystyle r^2}}\right]\times {10}^9\text{V},$ where the value of $\alpha$ is _______ . (Use $\frac{1}{4\pi {\epsilon }_0}=9\times {10}^9{\text{ Nm}}^2{\text{C}}^{-2}$)              [2024]

Q 3 :    

For a short dipole placed at origin O, the dipole moment P is along x-axis, as shown in the figure. If the electric potential and electric field at A are $V_0$ and $E_0$, respectively, then the correct combination of the electric potential and electric field, respectively, at point B on the y-axis is given by          [2025]

• $\frac{V_0}{2} \mathrm{and} \frac{E_0}{16}$

   

• zero and $\frac{E_0}{8}$

   

• zero and $\frac{E_0}{16}$

   

• $V_0 \mathrm{and} \frac{E_0}{4}$

   

Q 4 :    

An electric dipole is placed at a distance of 2 cm from an infinite plane sheet having positive charge density ${\sigma }_0$. Choose the correct option from the following.         [2025]

• Torque on dipole is zero and net force is directed away from the sheet.

   

• Torque on dipole is zero and net force acts towards the sheet.

   

• Potential energy of dipole is minimum and torque is zero.

   

• Potential energy and torque both are maximum.

   

Q 5 :    

Two point charges –4 $\mu \mathrm{C}$ and 4 $\mu \mathrm{C}$, constituting an electric dipole, are placed at (–9, 0, 0) cm and (9, 0, 0) cm in a uniform electric field of strength ${10}^4$ ${\mathrm{NC}}^{-1}$. The work done on the dipole in rotating it from the equilibrium through 180° is           [2025]

• 14.4 mJ

   

• 18.4 mJ

   

• 12.4 mJ

   

• 16.4 mJ

   

Q 6 :    

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R)

Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.

Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.

In the light of the above statements, choose the most appropriate answer from the options given below:          [2025]

• (A) is correct but (R) is not correct.

   

• Both (A) and (R) are correct but (R) is not the correct explanation of (A).

   

• Both (A) and (R) are correct and (R) is the correct explanation of (A).

   

• (A) is not correct but (R) is correct.

   

Q 7 :    

A dipole with two electric charges of 2 $\mu$C magnitude each, with separation distance 0.5 $\mu$m, is placed between the plates of a capacitor such that its axis is parallel to an electric field established between the plates when a potential difference of 5 V is applied. Separation between the plates is 0.5 mm. If the dipole is rotated by 30° from the axis, it tends to realign in the direction due to a torque. The value of torque is :          [2025]

• $5\times {10}^{–9 }\mathrm{Nm}$

   

• $5\times {10}^{–3 }\mathrm{Nm}$

   

• $2.5\times {10}^{–12 }\mathrm{Nm}$

   

• $2.5\times {10}^{–9 }\mathrm{Nm}$

   

Q 8 :    

An electric dipole of dipole moment $6\times {10}^{–6}$ cm is placed in uniform electric field of magnitude ${10}^6$ V/m. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ______ J.          [2025]