Q. No.Two short electric dipoles \(A\) \(B\) \(P_1\) \(P_2\) \(x\) \(60^\circ\) \(x\) \(P_2/P_1\)
1. \(\dfrac{\sqrt{3}}{2}\)
2. \(2 \sqrt{3}\)
3. \(\dfrac{1}{\sqrt{3}}\)
4. \(\sqrt{3}\)
1. \(\dfrac{\sqrt{3}}{2}\)
2. \(2 \sqrt{3}\)
3. \(\dfrac{1}{\sqrt{3}}\)
4. \(\sqrt{3}\)
Subtopic: Electric Dipole |
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Two shorts dipoles \((A,B),\) \(A\) having charges \(\pm 2~ \mu \text{C}\) and length \(1~\text{cm}\) and \(B\) having charges \(\pm 4~ \mu \text{C}\) and length \(1~\text{cm}\) are placed with their centres \(80~\text{cm}\) apart as shown in the figure. The electric field at a point \(P\), equi-distant from the centres of both dipoles is: (in N/C)
1. \(\dfrac{9}{16} \sqrt{2} \times 10^5\)
2. \(4.5 \sqrt{2} \times 10^4\)
3. \(9 \sqrt{2} \times 10^4\)
4. \(\dfrac{9}{16} \sqrt{2} \times 10^4\)
1. \(\dfrac{9}{16} \sqrt{2} \times 10^5\)
2. \(4.5 \sqrt{2} \times 10^4\)
3. \(9 \sqrt{2} \times 10^4\)
4. \(\dfrac{9}{16} \sqrt{2} \times 10^4\)
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Three charges \(+2 q ,+3 q\). and \(-4q\) are situated at \((0,-3{a}),(2{a}, 0)\) and \((-2{a}, 0)\) respectively in the \(xy\) plane. The resultant dipole moment about origin is:
1. \(2 q a(3 \hat{j}-\hat{i})\)
2. \(2 q a(3 \hat{i}-7 \hat{j})\)
3. \(2 q a(7 \hat{i}-3 \hat{j})\)
4. \(2 q a(3 \hat{j}-7 \hat{i})\)
1. \(2 q a(3 \hat{j}-\hat{i})\)
2. \(2 q a(3 \hat{i}-7 \hat{j})\)
3. \(2 q a(7 \hat{i}-3 \hat{j})\)
4. \(2 q a(3 \hat{j}-7 \hat{i})\)
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Two small spherical balls of mass \(10 ~g \) each with charges \(-2 ~\mu \text{C} \) and \(2~ \mu \text{C},\) are attached to two ends of very light rigid rod of length \(20 ~\text{cm.}\) The arrangement is now placed near an infinite nonconducting charge sheet with uniform charge density of \(100 ~\mu \text{C/m}^2 \) such that length of rod makes an angle of \(30^\circ\) with electric field generated by charge sheet. Net torque acting on the rod is: (Take \(\varepsilon_0: 8.85 \times 10^{-12} ~\text{C}^2 / \text{Nm}^2 \))
1. \(1.12~\text{Nm} \)
2. \(2.24~\text{Nm} \)
3. \(112~\text{Nm} \)
4. \(11.2~\text{Nm} \)
1. \(1.12~\text{Nm} \)
2. \(2.24~\text{Nm} \)
3. \(112~\text{Nm} \)
4. \(11.2~\text{Nm} \)
Subtopic: Electric Dipole |
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A dipole with two electric charges of \(2~ \text{μC }\) magnitude each, with separation distance \(0.5~ \text{μm},\) 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 \(5~ \text V\) is applied. Separation between the plates is \(0.5~\text{mm.}\) If the dipole is rotated by \(30^\circ \) from the axis, it tends to realign in the direction due to a torque. The value of torque is:
1. \(5.0 \times 10^{-3}~ \text{Nm} \)
2. \(2.5 \times 10^{-9} ~\text{Nm}\)
3. \(5.0 \times 10^{-9} ~\text{Nm}\)
4. \(2.5 \times 10^{-12} ~\text{Nm}\)
1. \(5.0 \times 10^{-3}~ \text{Nm} \)
2. \(2.5 \times 10^{-9} ~\text{Nm}\)
3. \(5.0 \times 10^{-9} ~\text{Nm}\)
4. \(2.5 \times 10^{-12} ~\text{Nm}\)
Subtopic: Electric Dipole |
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Given below are two statements:
In the light of the above statements, choose the most appropriate answer from the options given below:
| 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. |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |
Subtopic: Electric Dipole |
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An electric dipole of dipole moment \(6 \times 10^{-6} \text{cm}\) is placed in a uniform electric field of magnitude \(10^6 ~\text{V/m} .\) 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:
1. \(79~\text J\)
2. \(102~\text J\)
3. \(54~\text J\)
4. \(12~\text J\)
1. \(79~\text J\)
2. \(102~\text J\)
3. \(54~\text J\)
4. \(12~\text J\)
Subtopic: Electric Dipole |
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Two point charges \(-4~\mu\text C\) and \(4~\mu\text C,\) constituting an electric dipole, are placed at \((-9,~0,~0)\) cm and \((9,~0,~0)\) cm in a uniform electric field of strength \(104 \text { NC}^{-1}.\) The work done on the dipole in rotating it from the equilibrium through \(180^\circ\) is:
1. \(12.4~\text{mJ}\)
2. \(16.4~\text{mJ}\)
3. \(14.4~\text{mJ}\)
4. \(18.4~\text{mJ}\)
1. \(12.4~\text{mJ}\)
2. \(16.4~\text{mJ}\)
3. \(14.4~\text{mJ}\)
4. \(18.4~\text{mJ}\)
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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:
Choose the correct option from the following:
| 1. | Potential energy and torque both are maximum |
| 2. | Torque on dipole is zero and net force is directed away from the sheet |
| 3. | Torque on dipole is zero and net force acts towards the sheet |
| 4. | Potential energy of dipole is minimum and torque is zero |
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An electric dipole of mass \(m,\) charge \(q,\) and length \(l\) is placed in a uniform electric field
1. \(\dfrac{1}{2 \pi} \sqrt{\dfrac{2 {ml}}{{qE}_0}}\)
2. \(2 \pi \sqrt{\dfrac{m l}{2 q E_0}}\)
3. \(2 \pi \sqrt{\dfrac{m l}{q E_0}}\)
4. \(\dfrac{1}{2 \pi} \sqrt{\dfrac{m l}{2 q E_0}}\)
1. \(\dfrac{1}{2 \pi} \sqrt{\dfrac{2 {ml}}{{qE}_0}}\)
2. \(2 \pi \sqrt{\dfrac{m l}{2 q E_0}}\)
3. \(2 \pi \sqrt{\dfrac{m l}{q E_0}}\)
4. \(\dfrac{1}{2 \pi} \sqrt{\dfrac{m l}{2 q E_0}}\)
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