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Q. No.A thin uniform rod of mass \(M\) and length \(L\) is suspended from one of its ends, '\(A\)', so that it can rotate freely about it. A charge '\(q\)' is fixed to its lower end \(B\). A uniform horizontal Electric field is switched on and the rod rotates about \(A\), finally coming to equilibrium – making an angle of \(45^{\circ}\) with the vertical. If the acceleration due to gravity is '\(g\)', then,
1. \(qE =Mg\)
2. \(2qE =Mg\)
3. \(qE =2Mg\)
4. \(\sqrt{2}qE =Mg\)
Subtopic: Electric Field |
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Two very long insulated glass rods are charged uniformly by giving them identical charges '\(q\)', each. The rods have lengths \(L\) each and are placed parallel to each other at a distance '\(r\)' apart, where \(r\ll L\). Then, the electric force acting between the rods is proportional to:
| 1. | \(\dfrac{1}{r^2}\) | 2. | \(\dfrac{1}{r}\) |
| 3. | \(r\) | 4. | \(\dfrac{1}{r^3}\) |
Subtopic: Electric Field |
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A point charge '\(q\)' is placed at the centre of a spherical cavity at the centre of a conducting sphere. The sphere is initially uncharged. The radius of the cavity is '\(a\)' and that of the sphere is '\(2a\)'. Let the charge on the outer surface of the sphere be \(Q\).
Then,
Then,
| 1. | \(q,Q\) are of the same sign and \(|q|=|Q|\) |
| 2. | \(q,Q\) are of opposite signs and \(|q|=|Q|\) |
| 3. | \(q,Q\) are of the same sign and \(|q|<|Q|\) |
| 4. | \(q,Q\) are of opposite signs and \(|q|>|Q|\) |
Subtopic: Gauss's Law |
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A uniformly charged sphere carrying a charge \(Q\) distributed uniformly on its outer surface is placed in an isotropic medium of dielectric constant '\(K\)'.
The electric field within the medium due to the charge \(Q\) at some point \(P\) is \(\vec E_{Q}\). The Electric field at the same point \(P\) due to induced charge within the medium is \(\vec E_{m}\). Then,
The electric field within the medium due to the charge \(Q\) at some point \(P\) is \(\vec E_{Q}\). The Electric field at the same point \(P\) due to induced charge within the medium is \(\vec E_{m}\). Then,
| 1. | \(|\vec E_m|=\left|\dfrac{\vec E_Q}{K}\right|,\) and the two fields are in opposite directions. |
| 2. | \(|\vec E_Q|=\left|\dfrac{\vec E_m}{K}\right|,\) and the two fields are in the same direction. |
| 3. | \(|\vec E_Q+\vec E_m|=\left|\dfrac{\vec E_Q}{K}\right|,\) and the two fields are in opposite directions. |
| 4. | \(|\vec E_Q+\vec E_m|=\left|\dfrac{\vec E_m}{K}\right|,\) and the two fields are in the same direction. |
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.
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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Three charges \(q,~q,~-q\) are placed at the three corners of an equilateral triangle \(ABC\), of side \(a.\)
The mid-point of side \(AB\) is \(P\) while the circumcenter of \(ABC\) is \(O\). Let the electric field at \(P\) be \(E_p\) and that at \(O\) be \(E_O.\)
Then, \(E_O:E_P=\)
The mid-point of side \(AB\) is \(P\) while the circumcenter of \(ABC\) is \(O\). Let the electric field at \(P\) be \(E_p\) and that at \(O\) be \(E_O.\)
Then, \(E_O:E_P=\)
| 1. | \(\dfrac{2}{9}\) | 2. | \(\dfrac{4}{9}\) |
| 3. | \(\dfrac{9}{2}\) | 4. | \(\dfrac{9}{4}\) |
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. \(7 \sqrt 2~\text{V/m}\)
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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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 |
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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 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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