Question

The angle between the electric lines of force and the equipotential surface is:

• A. 0°
• B. 45°
• C. 90°
• D. 180°

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
An equipotential surface is defined as a surface where the electric potential (\(V\)) is the same at every point.
Electric lines of force (field lines) show the direction of the electric field (\(\vec{E}\)).
Step 2: Detailed Explanation:
Consider a small displacement \(d\vec{l}\) along an equipotential surface.
By definition, the change in potential \(dV\) is zero.
The relationship between electric field and potential is:
\[ dV = -\vec{E} \cdot d\vec{l} \]
Since \(dV = 0\) for any displacement along the surface:
\[ \vec{E} \cdot d\vec{l} = 0 \]
From the properties of the dot product:
\[ E dl \cos \theta = 0 \]
Since neither \(E\) nor \(dl\) is zero, \(\cos \theta\) must be zero, which means \(\theta = 90^\circ\).
This proves that the electric field (\(\vec{E}\)) is always perpendicular to the equipotential surface at every point.
Step 3: Final Answer:
The angle is \(90^\circ\).