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
View Answer
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
View Answer
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
View Answer
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
View Answer
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
View Answer
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.
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
View Answer
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): In a given situation of arrangement of charges, an additional charge is placed outside the Gaussian surface. In this situation, in the Gauss theorem \(\oint \vec{E}.d\vec{s} = \frac{q_{in}}{\epsilon_0}\) remains unchanged whereas electric field \(vec{E}\) is changed.
Reason (R): Electric field \(\vec{E}\) at any point on the Gaussian surface is due to inside charge only.
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. An external charge does not change the net charge enclosed by the Gaussian surface \(q_{in}\), so the total electric flux \(\oint \vec{E}.d\vec{s}\) remains unchanged as per Gauss's Law. However, the electric field \(\vec{E}\) at any point on the surface is the vector sum of fields from all charges, both inside and outside, so it will change. Reason (R) is false because the electric field at any point is due to both internal and external charges.
Assertion (A): Angular momentum of the two dipole system is not conserved.
Reason (R): There is a net torque on the system.
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
For an isolated system of two dipoles, the torques they exert on each other are internal forces. Internal torques within a system cancel each other out, leading to zero net torque on the system. Therefore, according to the conservation of angular momentum \(\frac{d\vec{L}}{dt} = \vec{\tau}_{ext}\)), if the net external torque is zero, the angular momentum of the system is conserved. Hence, both assertion (A) and reason (R) are false.
Assertion (A): Continuity equation explains conservation of electric charge.
Reason (R): Gauss law shows diversion when inverse square law is not obeyed.
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
View Answer
Continuity equation describes conservation of charge. Gauss's law is a fundamental law valid irrespective of the inverse square law and does not show 'diversion' based on its obedience. Thus, (A) is true, (R) is false.
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
View Answer
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).