Q. No.Given below are two statements:
| Assertion (A): | The electrostatic field of a charge distributed uniformly over the surface of a sphere vanishes within the sphere, only at its centre. |
| Reason (R): | This cancellation occurs at the centre due to the symmetry of the sphere and the symmetric, uniform charge distribution. |
| 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 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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Hints
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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 |
From NCERT
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Three identical charges (\(q\) each) are placed at the three vertices \(A,B,C\) of an equilateral triangle of side \(a.\) Let \(O\) be the centre (centroid) of the triangle \(ABC\) and \(O'\) be the reflection of \(O\) in \(BC.\) The electric field at \(O,\) due to any one of the charges, is \(E.\) The net field at \(O',\) due to all the three charges, is:
| 1. | \(2E\) | 2. | \(\Large\frac{3E}{2}\) |
| 3. | \(\Large\frac{4E}{3}\) | 4. | \(\Large\frac{5E}{4}\) |
Subtopic: Electric Field |
From NCERT
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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. \(\sqrt{2}qE =Mg\)
1. \(qE =Mg\)
2. \(2qE =Mg\)
3. \(qE =2Mg\)
4. \(\sqrt{2}qE =Mg\)
Subtopic: Electric Field |
From NCERT
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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 |
From NCERT
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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 |
From NCERT
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Given below are two statements:
| Assertion (A): | The electrostatic field of a charge on a spherical conductor is identical to that of an equal charge placed at its centre. |
| Reason (R): | Any charge given to a spherical conductor distributes itself uniformly on its surface, and this results in the field of a uniformly charged thin spherical shell. |
| 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 Field |
From NCERT
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An infinitely long straight line carries a uniform positive charge \(\lambda\) per unit length. A negative point charge \((-q)\) moves in a circular path with the charge \(\lambda\) as its axis, under the action of its electric field. The kinetic energy of the point charge is:
| 1. | \({\dfrac{q\lambda}{4\pi\varepsilon_0}}\) | 2. | \({\dfrac{q\lambda}{2\pi\varepsilon_0}}\) |
| 3. | \({\dfrac{2q\lambda}{\pi\varepsilon_0}}\) | 4. | \({\dfrac{q\lambda}{8\pi\varepsilon_0}}\) |
Subtopic: Electric Field |
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A small conducting sphere of variable radius is given a charge \(q.\) Consider the electrostatic field at a point \(P\) outside this sphere, due to the charge.
As the radius of the sphere is slowly increased (like a balloon inflating), the electric field at \(P\):
As the radius of the sphere is slowly increased (like a balloon inflating), the electric field at \(P\):
| 1. | remains constant in magnitude and direction. |
| 2. | increases in magnitude, but retains its direction. |
| 3. | decreases in magnitude, but retains its direction. |
| 4. | changes in magnitude and direction. |
Subtopic: Electric Field |
From NCERT
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