Rankers Physics

Electric Potential: Practice Problem & Solution

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.  
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

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:

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).

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