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Question

Electric field in a region is $\vec E = 3\hat j\,N/C$. Equipotential surfaces are parallel to

VENKATESWARARAO · Accepted Answer

## CORE INFORMATION
✓ **Answer**: B
## CONCEPT FRAMEWORK
	**Primary Concept**: Relationship between electric field and equipotential surfaces.
	**Related Topics**: Electric field vectors, Potential difference, Gradient of potential.
	**Prerequisites**: Understanding of electric fields, potential, and their relationship.
## SOLUTION PATHWAY
**Given Information**:
	* Electric field vector $\vec E = 3\hat j\,N/C$.
	* We need to find the orientation of equipotential surfaces.
**Method & Steps**:
	1. **Understanding the relationship**: Equipotential surfaces are always perpendicular to the electric field lines. This is because the electric field does no work when a charge moves along an equipotential surface. The electric field is the negative gradient of the potential, i.e.  $\vec E = - 
abla V$.
		Reasoning: The potential change is zero along equipotential surfaces, and the electric field points in the direction of the steepest decrease in potential.
		Formula/Rule: $\vec E \cdot d\vec l = 0$ along an equipotential surface.
	2. **Analyzing the given electric field**: The electric field $\vec E = 3\hat j$ points only in the y-direction.
		Working: This means the direction of the electric field is along the y-axis.
		Key Point:  Equipotential surfaces must be perpendicular to the y-axis.
	3. **Determining the surface orientation**: A plane perpendicular to the y-axis is the xz-plane.
		Result:  The equipotential surfaces are parallel to the xz-plane.
		Verification: If the equipotential surfaces are in the xz plane, then any displacement in that plane will result in no change in potential. Since the electric field is in the y direction, then the dot product of the electric field and a displacement in the xz plane will be zero, which is consistent with the definition of an equipotential surface.
 ## OPTION ANALYSIS
[A] :x:  xy plane would not be perpendicular to the y-directed electric field.
[B] ✓: xz plane is perpendicular to the y-directed electric field.
[C] :x: yz plane would not be perpendicular to the y-directed electric field.
[D] :x: Only the xz plane is perpendicular to the y-directed electric field.
 ## LEARNING AIDS
	**Common Mistakes**:
		1.  Confusing parallel and perpendicular: Students might incorrectly think equipotential surfaces are parallel to the electric field.
			How to avoid: Remember that electric fields do no work along equipotential surfaces, which means they are always perpendicular.
	**Quick Tips**:
		1.  Visualize the electric field lines and equipotential surfaces as being perpendicular to each other.
		2.  If the electric field is along one axis, the equipotential surfaces are perpendicular to that axis.

VENKATESWARARAO · Answer

xy plane

VENKATESWARARAO · Answer

The correct Option is "xz plane"

VENKATESWARARAO · Answer

yz plane

VENKATESWARARAO · Answer

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