Assertion (A): The whole charge of a conductor cannot be transferred to another conductor.
Reason (R): The total transfer of charge from one to another is not possible.
Both (A) and (R) are false. Charge can be completely transferred between conductors, for example, by induction or conduction, if placed inside a hollow conductor and connected.
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.
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.
Assertion (A): A point charge is brought in an electric field. The field at a nearby point will increases, whatever be the nature of charge.
Reason (R): The direction of electric field lines is independent of the nature of charge.
Both (A) and (R) are false. The resultant electric field can increase, decrease or cancel depending on vector sum. Field line direction depends on charge sign.
Assertion (A): If a point charge be rotated in a circle around another stationary charge at the centre of the circle, the work done by electric field will be zero.
Reason (R): Work done by centripetal force is always zero.
Both (A) and (R) are true. (A) is true because the electric field is conservative and the path is equipotential. (R) is true as centripetal force is perpendicular to displacement (\(W = Fdr\cos 90^\circ = 0\)). However, (R) does not explain (A).
Assertion (A): Electrostatic field inside a conducting shell is always zero.
Reason (R): The electrostatic potential is always same from center to surface of a conducting shell.
Concept: Properties of conductors in electrostatic equilibrium.
Formula: \( \vec{E} = -\nabla V \).
Solution: In a conductor, free charges redistribute to make \( \vec{E} = 0 \) inside (A is true). If \( \vec{E} = 0 \) inside, then \( V \) must be constant (R is true) and thus (R) correctly explains (A).
The electrostatic potential on the surface of a charged solid conducting sphere is 100 volts. Two statements are made in this regard :
Assertion (A): At any point inside the sphere, electrostatic potential is 100 volt.
Reason (R): At any point inside the sphere, electric field is zero.
Concept: Properties of charged conductors.
Principle: Inside a conductor, \( \vec{E} = 0 \) and \( V = \text{constant} \).
Solution: For a solid conducting sphere, potential is uniform throughout its volume and equals surface potential (A is true). This is because the electric field inside a conductor is zero (R is true), implying constant potential. Thus, (R) correctly explains (A).
Assertion (A): If electric field in x-y plane is given by \( \vec{E} = y\hat{i} + x\hat{j} \) then equipotential curve is given by \( xy = \text{ constant} \).
Reason (R): Electric field may not be perpendicular to equipotential surface/curve/line.
Concept: Relation between electric field and equipotential surfaces.
Formula: \( \vec{E} = -\nabla V \).
Solution: From \( \vec{E} = -\nabla V \) for \( \vec{E} = y\hat{i} + x\hat{j} \), potential is \( V = -xy + C \), so equipotential curves are \( xy = \text{ constant} \) (A is true). Electric field lines are always perpendicular to equipotential surfaces (R is false).
Assertion (A): Distance of closest approach for free target is more than that for fixed target.
Reason (R): Total energy is conserved for free target but not for fixed target.
For a free target, kinetic energy is shared, reducing the effective kinetic energy, leading to a larger closest approach distance (A is true). For a free target, mechanical energy of interacting particles is conserved. For a fixed target, external forces do work, so mechanical energy of the interacting particles is not conserved (R is true). This difference explains (A).
Assertion (A): When an isolated charged body is connected to earth, all its charge flows to earth and it becomes electrically neutral.
Reason (R): Electric potential of earth is non zero, so the body connected to earth should also attain zero potential.
Assertion (A) is true as charges flow to earth. Reason (R) is false because earth's potential is considered zero.
Assertion (A): Potential difference between two points in space is zero if electric field at all points in space is zero.
Reason (R): Electric field E at a point P is zero if potential at that point is zero.
Concept: Relation between electric field and potential.
Formula: \( \Delta V = -\int \vec{E} \cdot d\vec{l} \). If \( \vec{E} = 0 \), then \( \Delta V = 0 \).
Solution: If \( \vec{E} = 0 \) everywhere, then potential is constant, so \( \Delta V = 0 \) (A is true). If \( V=0 \) at a point, \( \vec{E} \) is not necessarily zero (e.g., center of a dipole) (R is false).