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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 |
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A point charge \(q\) is placed at the centre of the flat surface of a semi-infinite cylinder of radius \(r.\) The flux of its electric field through the curved surface of the cylinder is:
| 1. | \(\dfrac{q}{\varepsilon_0}\) | 2. | \(\dfrac{q}{2\varepsilon_0}\) |
| 3. | \(\dfrac{2q}{\varepsilon_0}\) | 4. | \(0\) |
Subtopic: Gauss's Law |
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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 |
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Two identical balls of cork \(\mathrm{(C_1,C_2)}\) are charged oppositely with equal amounts of charge distributed uniformly over their respective surfaces. Two similar (of same size) balls of copper\((M_1,M_2)\) are charged in the same way as the previous two balls. \(\mathrm{C_1,C_2}\) are allowed to touch each other briefly and are separated, and the same is done with \(M_1,M_2.\) The electrostatic force between \(\mathrm{C_1,C_2}\) is \(F_C\) and that between \(M_1,M_2\) is \(F_M\) at the same separation. Then:
| 1. | \(F_C=0,F_M\neq0\) | 2. | \(F_C\neq0,F_M=0\) |
| 3. | \(F_C=0,F_M=0\) | 4. | \(F_C\neq0,F_M\neq0\) |
Subtopic: Electric Charge |
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Consider an \(HCl\) molecule, where one of its electrons is located exactly midway between the two nuclei, at a given instant. Ignore all the other electrons and any quantum effects.
Let \(\vec F_H\) be the electrostatic force exerted by the electron on the \(H\)-nucleus and \(\vec F_{Cl}\) be the force exerted by the electron on the \(Cl\) nucleus. Then:
Let \(\vec F_H\) be the electrostatic force exerted by the electron on the \(H\)-nucleus and \(\vec F_{Cl}\) be the force exerted by the electron on the \(Cl\) nucleus. Then:
| 1. | \(|\vec F_{Cl}|=|\vec F_H|\)and \(\vec F_{Cl}\) is opposite to \(\vec F_H\) |
| 2. | \(|\vec F_{Cl}|=|\vec F_H|\)and \(\vec F_{Cl}\) & \(\vec F_H\) are in the same direction |
| 3. | \(|\vec F_{Cl}|>|\vec F_H\) and \(\vec F_{Cl}\) is opposite to \(\vec F_H\) |
| 4. | \(|\vec F_{Cl}|<|\vec F_H|\) and \(\vec F_{Cl}\) is opposite to \(\vec F_H\) |
Subtopic: Coulomb's Law |
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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 |
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A point charge \(q\) (positive) is placed just below the centre \(O\) of the top face of a cylinder of height \(h,\) and radius \(r:\) \(h\gg r.\) The flux of the electric field of the charge \(q\) through the top face is \(\phi_t,\) through the bottom face is \(\phi_b\) and through the curved face of the cylinder is \(\phi_c.\) Then, one can conclude,
1. \(\phi_t<\phi_c<\phi_b\)
2. \(\phi_t<\phi_b<\phi_c\)
3. \(\phi_t>\phi_c>\phi_b\)
4. \(\phi_t>\phi_b>\phi_c\)
1. \(\phi_t<\phi_c<\phi_b\)
2. \(\phi_t<\phi_b<\phi_c\)
3. \(\phi_t>\phi_c>\phi_b\)
4. \(\phi_t>\phi_b>\phi_c\)
Subtopic: Gauss's Law |
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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 |
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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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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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