Assertion (A): A metal sphere of radius \(1\text{ cm}\) cannot hold a charge of \(1\text{ coulomb}\) in air.
Reason (R): The dielectric strength of air (minimum field required for ionisation of a medium) is \(3\text{ MV/m}\).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true: \(1\text{ C}\) is a huge charge for a \(1\text{ cm}\) sphere.
Reason (R) is true: Air's dielectric strength is \(3 \times 10^6\text{ V/m}\). The electric field at the surface \(E = \frac{Q}{4\pi \epsilon_0 R^2}\text{ }\approx 9 \times 10^{13}\text{ V/m}\).
This field greatly exceeds air's dielectric strength, causing electrical breakdown. Thus, (R) explains (A).
Assertion (A): In any electrostatic field, a charge cannot be in stable equilibrium.
Reason (R): An electrostatic field is a conservative force field.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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According to Earnshaw's Theorem, a charge cannot be in stable equilibrium in an electrostatic field, thus Assertion (A) is true. An electrostatic field is a conservative force field, so Reason (R) is true. However, the conservative nature of the field is not the direct explanation for Earnshaw's theorem, which is derived from Gauss's law and the Laplace equation.
Assertion (A): If a proton and an electron are placed in the same uniform electric field one by one, they experience different accelerations (The only force acting on proton and electron is that exerted by uniform electric field).
Reason (R): Electric force on a test charge is independent of its mass.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true because \(a = F/m\). In a uniform electric field \(E\), the magnitude of force on both proton and electron is \(F = eE\). Since their masses are different (\(m_e \neq m_p\)), their accelerations \(a\) will be different. Reason (R) is true as the electric force \(F = qE\) depends on charge \(q\) and electric field \(E\), not mass \(m\). Reason (R) correctly explains Assertion (A).
Assertion (A): When a negative charge \(-q\) is released at a distance \(R\) from the centre and along the axis of a uniformly and positively charged fixed ring of radius \(R\), the negative charge does oscillation but not SHM.
Reason (R): The force on negative charge is always towards the centre of the ring but it is not proportional to the displacement from the centre of the ring.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true. The electric force on charge \(-q\) on the axis of a positively charged ring is a restoring force towards the center, causing oscillation. The force is \(F = \frac{kQqx}{(R^2+x^2)^{3/2}}\). This is not linearly proportional to \(x\) (displacement) unless \(x \ll R\), so it's not SHM. Reason (R) is true. The force is attractive (towards center) and indeed not proportional to \(x\). Reason (R) correctly explains Assertion (A).
Assertion (A): There is an isolated system of two charged conducting spheres A and B. The resultant electric field at point P is the sum of electric field at P due to charged sphere A only (that is, assuming sphere B and all its effects to be absent) and the electric field at P only due to sphere B (that is, assuming sphere A and all its effects to be absent).
Reason (R): Superposition theorem for electric field due to point charges states that resultant electric field at a point due to point charges is the sum of electric field at that point due to individual charges.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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The electric field \(\vec{E}\) obeys the superposition principle. Assertion (A) accurately describes this principle for fields from multiple charge distributions. Reason (R) correctly states the superposition theorem. Hence, R correctly explains A.
Assertion (A): Electric field is always zero in a cavity inside a conductor.
Reason (R): All points in a cavity inside a conductor are always at same potential.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Assertion (A) is true for an uncharged cavity in electrostatic equilibrium (electrostatic shielding). Reason (R) is also true, as \(\vec{E} = -\nabla V\), so zero field implies constant potential. However, constant potential is a consequence of zero field, not its explanation.
Assertion (A): We cannot produce electric field in a neutral conductor.
Reason (R): Neutral conductor cannot produce electric field.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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In electrostatic equilibrium, the electric field inside a conductor is zero due to charge redistribution. A neutral conductor has no net charge, so it cannot be a source of electric field. Both assertion (A) and reason (R) are true, but (R) does not correctly explain (A); the zero field inside is due to charge mobility and redistribution, not simply its neutrality.
Assertion (A): A moving charge particle may gets energy from electric field.
Reason (R): Electric field works on moving charge.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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An electric field exerts a force \( \vec{F} = q\vec{E} \) on a charge `\( q \)`. If the charge moves, work \( W = \int \vec{F} \cdot d\vec{l} \) can be done, changing its energy. Hence, both are true and (R) explains (A).
Assertion (A): Electric field intensity at surface of a uniformly charged spherical shell is `\( E \)`. If shell is punctured at a point then intensity at punctured point becomes `\( E/2 \)`.
Reason (R): Electric field intensity due to a spherical charge distribution can be found out by using Gauss law.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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The field at a puncture is `\( E/2 \)` due to superposition. Gauss's law helps find the field for symmetric distributions, but it doesn't explain the `\( E/2 \)` effect at the puncture directly. Both (A) and (R) are true, but (R) is not the correct explanation of (A).
Assertion (A): At a point in space, the electric field points toward east. In the region, surrounding this point the potential will be constant along north and south.
Reason (R): Electric field at a point in space is proportional to rate of change of potential with distance.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true because equipotential surfaces are perpendicular to electric field lines. Reason (R) is true as \(E = -\frac{dV}{dr}\). However, (R) describes the relation, but not why potential is constant along north-south specifically for an eastward field.