Electric dipole and torque on a dipole — practice questions

Question 1 · difficulty L2 · understanding

A dipole with two electric charges of 2 µC magnitude each, with separation distance 0.5 µm, 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:

• A. 2.5×10 −9 Nm
• B. 2.5×10 −12 Nm
• C. 5×10 −3 Nm
• D. 5×10 −9 Nm

Question 2 · difficulty L2 · understanding

The electrostatic potential due to an electric dipole at a distance '$$r$$' varies as :

• A. $$\frac{1}{r^3}$$
• B. $$\frac{1}{\mathrm{r}}$$
• C. $$\frac{1}{r^2}$$
• D. r

Question 3 · difficulty L2 · understanding

Two charges each of magnitude $$0.01 ~\mathrm{C}$$ and separated by a distance of $$0.4 \mathrm{~mm}$$ constitute an electric dipole. If the dipole is placed in an uniform electric field '$$\vec{E}$$' of 10 dyne/C making $$30^{\circ}$$ angle with $$\vec{E}$$, the magnitude of torque acting on dipole is:

• A. $$4 \cdot 0 \times 10^{-10} ~\mathrm{Nm}$$
• B. $$1.5 \times 10^{-9} ~\mathrm{Nm}$$
• C. $$1.0 \times 10^{-8} ~\mathrm{Nm}$$
• D. $$2.0 \times 10^{-10} ~\mathrm{Nm}$$

Question 4 · difficulty L2 · understanding

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : If an electric dipole of dipole moment $$30 \times 10^{-5} ~\mathrm{C} ~\mathrm{m}$$ is enclosed by a closed surface, the net flux coming out of the surface will be zero. Reason R : Electric dipole consists of two equal and opposite charges. In the light of above, statements, choose the correct answer from the options given below.

• A. A is true but R is false
• B. A is false but R is true
• C. Both A and R are true but R is NOT the correct explanation of A
• D. Both A and R are true and R is the correct explanation of A

Question 5 · difficulty L2 · understanding

Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A) : Non-polar materials do not have any permanent dipole moment. Reason (R) : When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution. In the light of above statements, choose the most appropriate answer from the options given below.

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

Question 6 · difficulty L2 · understanding

An electric dipole of dipole moment $6 \times 10^{-6} \mathrm{Cm}$ is placed in uniform electric field of magnitude $10^{6} \mathrm{V} / \mathrm{m}$. 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.

Question 7 · difficulty L2 · understanding

The electric field at point $$\mathrm{p}$$ due to an electric dipole is $$\mathrm{E}$$. The electric field at point $$\mathrm{R}$$ on equitorial line will be $$\frac{\mathrm{E}}{x}$$. The value of $$x$$ :

Question 8 · difficulty L2 · understanding

An electric dipole of dipole moment is $$6.0 \times 10^{-6} ~\mathrm{C m}$$ placed in a uniform electric field of $$1.5 \times 10^{3} ~\mathrm{NC}^{-1}$$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $$180^{\circ}$$ in this field will be ___________ $$\mathrm{m J}$$.

Question 9 · difficulty L2 · understanding

Two electric dipoles of dipole moments $$1.2 \times 10^{-30} \,\mathrm{Cm}$$ and $$2.4 \times 10^{-30} \,\mathrm{Cm}$$ are placed in two different uniform electric fields of strengths $$5 \times 10^{4} \,\mathrm{NC}^{-1}$$ and $$15 \times 10^{4} \,\mathrm{NC}^{-1}$$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $$\frac{1}{x}$$. The value of $$x$$ is __________.

Question 10 · difficulty L3 · understanding

A rigid dipole undergoes a simple harmonic motion about its centre in the presence of an electric field $\overrightarrow{\mathrm{E}}_1=\mathrm{E}_0 \hat{x}$. If another electric field $\overrightarrow{\mathrm{E}}_2=2 \mathrm{E}_0(\hat{y}+\hat{z})$ is introduced to the system, what will be the percentage change in the frequency of the oscillation (approximate)?

• A. 73%
• B. 63%
• C. 83%
• D. 53%