Question

Equipotential surfaces

• A. are closer in regions of large electric fields compared to regions of lower electric fields.
• B. are closer in regions of lower electric fields compared to regions of large electric fields.
• C. will always be concentric spherical surfaces.
• D. will always be equally spaced.

Hint:

Remember: \[ E=-\frac{dV}{dr} \] \[ \text{Strong Electric Field} \Rightarrow \text{Closely Spaced Equipotential Surfaces} \] \[ \text{Weak Electric Field} \Rightarrow \text{Widely Spaced Equipotential Surfaces} \]

Answer 1

The Correct Option is A

Concept: The electric field is related to the potential gradient by \[ E=-\frac{dV}{dr} \] Thus, electric field strength is equal to the rate of change of potential with distance.

Step 1: Relate spacing of equipotential surfaces with electric field. For a given potential difference, \[ E=\frac{\Delta V}{\Delta r} \] Hence, \[ E\propto\frac{1}{\Delta r} \] where \(\Delta r\) is the separation between adjacent equipotential surfaces.

Step 2: Analyse regions of strong electric field. If the electric field is large, \[ E \uparrow \] then \[ \Delta r \downarrow \] Therefore, equipotential surfaces are closer together. \[ \boxed{\text{Statement (A) is true.}} \]

Step 3: Check the remaining statements. Statement (B) is opposite to the correct relation. \[ \boxed{\text{Statement (B) is false.}} \] Equipotential surfaces are not always spherical. \[ \boxed{\text{Statement (C) is false.}} \] Their spacing depends on the electric field and is generally not uniform. \[ \boxed{\text{Statement (D) is false.}} \]

Step 4: State the answer. \[ \boxed{ \text{Equipotential surfaces are closer in regions of stronger electric field.} } \] Hence, the correct option is \[ \boxed{(A)} \]