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Q. No.Two infinite line charges, carrying charges \(+\lambda,-\lambda\) (per unit length) are placed parallel to each other, a short distance \(a\) apart. The electric field at a distance r from one of the charges \((A P = r)\) is:
1.
constant
2.
proportional to \(\dfrac{1}{r}\)
3.
proportional to \(\dfrac{1}{r^2}\)
4.
proportional to \(\dfrac{1}{r^3}\)
Subtopic: Electric Field |
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Two identical point charges, \(q\) each, are placed at the opposite ends of a long diagonal of a cube. The flux of the electric field, due to these charges, out of the cube, is:
| 1. | \(\dfrac{q}{\varepsilon_0}\) | 2. | \(\dfrac{q}{2\varepsilon_0}\) |
| 3. | \(\dfrac{q}{4\varepsilon_0}\) | 4. | \(\dfrac{q}{8\varepsilon_0}\) |
Subtopic: Gauss's Law |
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Given below are two statements:
| Statement I: | Gauss's law for electric fields is a consequence of the conservation of energy. |
| Statement II: | Coulomb's law for electric charges leads to a conservative electric field. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Gauss's Law |
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An electric dipole of dipole moment \(p\) is placed at the centre of a spherical surface of radius \(R.\) The net flux of the electric field of the dipole through the hemisphere, where it is positive, is proportional to:
1. \(R\)
2. \(R^{-3}\)
3. \(R^{-2}\)
4. \(R^{-1}\)
1. \(R\)
2. \(R^{-3}\)
3. \(R^{-2}\)
4. \(R^{-1}\)
Subtopic: Gauss's Law |
From NCERT
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Equal and opposite charges are placed at the two vertices of an equilateral triangle, giving a dipole moment \(p.\) A small dipole \(p'\) is placed at the third vertex, parallel to the previous dipole. If the electric fields due to both dipoles \(p,~p',\) at the mid-point of the dipole \(p,\) are equal, then \(\dfrac{p'}{p}\) equals:
| 1. | \(3\sqrt3\) | 2. | \(\dfrac{3\sqrt3}{2}\) |
| 3. | \(\sqrt3\) | 4. | \(\dfrac{\sqrt3}{2}\) |
Subtopic: Electric Dipole |
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A point charge \(q\) is placed within a spherical cavity inside a metallic conductor, slightly off-centre. The charge \(q\) induces a charge distribution on the inner surface of the cavity. The net force on \(q\) due to the induced charges is:
| 1. | zero |
| 2. | towards the centre |
| 3. | away from the centre |
| 4. | either towards or away from the centre depending on the sign of \(q\) |
Subtopic: Gauss's Law |
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A dipole is placed at the centre of a uniformly charged circular ring, with the axis of the dipole along the axis of the ring.
The dipole experiences:
1. no force and no torque.
2. a force but no torque.
3. a torque but no force.
4. a force and a torque.
The dipole experiences:
1. no force and no torque.
2. a force but no torque.
3. a torque but no force.
4. a force and a torque.
Subtopic: Electric Dipole |
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A uniformly charged circular ring (of radius \(R\)) has a total charge \(Q;\) a second point charge \(q\) is placed at the center of the ring. Consider a point \(P\) on the axis of the ring, at a distance \(x\) from its center. The radius of the ring subtends an angle \(\theta\) at the point \(P.\)
If the net electric field at \(P\) is zero, then:
1. \(\cos\theta=\Big|\dfrac qQ\Big|\)
2. \(\cos^2\theta=\Big|\dfrac qQ\Big|\)
3. \(\cos^3\theta=\Big|\dfrac qQ\Big|\)
4. \(\cos^{\frac12}\theta=\Big|\dfrac qQ\Big|\)
If the net electric field at \(P\) is zero, then:
1. \(\cos\theta=\Big|\dfrac qQ\Big|\)
2. \(\cos^2\theta=\Big|\dfrac qQ\Big|\)
3. \(\cos^3\theta=\Big|\dfrac qQ\Big|\)
4. \(\cos^{\frac12}\theta=\Big|\dfrac qQ\Big|\)
Subtopic: Electric Field |
From NCERT
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An electric field is given by: \(\vec{E}(x,~y)=4 x \hat{\imath}-3 y \hat{\jmath}\); the field being measured in \(\text{'V/m'}\) and the distances in \(\text{'m'}.\) The variation of the potential along the direction \((\hat i - \hat j)\) at the point \((2, 2)\) is given by:
1. \(-14 ~\text{V/m}\)
2. \(14 ~\text{V/m}\)
3. -\(7 \sqrt 2~\text{V/m}\)
4. \(7 \sqrt 2~\text{V/m}\)
1. \(-14 ~\text{V/m}\)
2. \(14 ~\text{V/m}\)
3. -\(7 \sqrt 2~\text{V/m}\)
4. \(7 \sqrt 2~\text{V/m}\)
Subtopic: Electric Field |
From NCERT
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Which of the following field configurations is/are possible?
Note: \(A,B,C\) are conductors. Other charges may be present in the vicinity.
Note: \(A,B,C\) are conductors. Other charges may be present in the vicinity.
| 1. | I, III | 2. | II |
| 3. | I, II, III | 4. | none of I, II, III |
Subtopic: Electric Field |
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