Electric Potential: Practice Problem & Solution
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 \( \vec{E} \) at a point \( P \) is zero if potential at that point is zero.
Short Solution (Best for NEET):
To solve this problem, we apply the core principles of Electric Potential. Understanding the underlying formula is key to arriving at the correct answer below:
If \( \vec{E} = \vec{0} \) everywhere, then \( \vec{E} = -\nabla V = \vec{0} \), implying \( V \) is constant, so \( \Delta V = 0 \). However, \( V = 0 \) at a point does not imply \( \vec{E} = \vec{0} \) (e.g., at the center of an electric dipole). Thus (A) is true and (R) is false.
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