Assertion (A): We can shield a charge from electric fields by putting it inside a hollow conductor but we can not shield a body from the gravitational influence of near by matter by putting it inside a hollow sphere.
Reason (R): Gravitational force in between two point mass bodies is independent of the intervening medium them.
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: Electrostatic shielding (Faraday cage) works, but gravitational shielding does not. Reason (R) is true: Gravitational force is a fundamental interaction that is unaffected by the medium. (R) correctly explains (A) as electric fields can be screened by charge redistribution in conductors, a mechanism not available for gravity.
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): The electric field due to point charge configuration with total charge zero is not zero.
Reason (R): Gauss law does not hold for a configuration with total charge zero.
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: an electric dipole (total charge zero) produces a non-zero electric field \(\propto 1/r^3\). Reason (R) is false: Gauss's Law \( \oint \vec{E} \cdot d\vec{A} = Q_{enc}/\epsilon_0\) is a fundamental law that always holds, regardless of the total charge.
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): If a charge is released from rest in an electric field, it will always move along an electric field line.
Reason (R): Force on a charged particle is always in the direction of 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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Assertion (A) is false; a particle released from rest follows a field line only if it is straight. If the field line is curved, inertia causes deviation. Reason (R) is false; for a negative charge, the force \(\vec{F} = q\vec{E}\) is opposite to the electric field \(\vec{E}\). Thus, both A and R are false.
Assertion (A): A charged particle is free to move in an electric field. It may or may not move along an electric line of force.
Reason (R): Initial conditions affect the motion of charged particle.
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; a charged particle's path in an electric field depends on its initial velocity and the field's curvature. Reason (R) is also true, as the initial velocity and position are crucial 'initial conditions' determining the trajectory. Reason (R) directly explains why the particle's path may or may not follow a field line.