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.

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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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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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. \(R^{-1}\)
Subtopic:  Gauss's Law |
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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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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. \(\cos^{\frac12}\theta=\Big|\dfrac qQ\Big|\)
Subtopic:  Electric Field |
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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.  \(7 \sqrt 2~\text{V/m}\)

 
Subtopic:  Electric Field |
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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.
1. I, III 2. II
3. I, II, III 4. none of I, II, III
Subtopic:  Electric Field |
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