Rankers Physics
Topic: Electrostatics
Subtopic: Electric Potential

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.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

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).

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