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Equipotential surfaces...

Equipotential surfaces

A

are closer in regions of large electric fields compared to regions of lower electric field

B

will be more crowded near sharp edges of a conductor.

C

will be m ore crowded near regions of large charge densities

D

will always be equally spaced.

Text Solution

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The correct Answer is:
To solve the question regarding equipotential surfaces, we need to understand the relationship between electric field intensity and the separation of these surfaces. Let's break this down step by step. ### Step-by-Step Solution: 1. **Understanding Equipotential Surfaces**: - Equipotential surfaces are surfaces where the electric potential is the same at every point. No work is done when moving a charge along an equipotential surface. 2. **Relationship Between Electric Field and Equipotential Surfaces**: - The electric field (E) is related to the potential (V) by the equation: \[ E = -\frac{dV}{dr} \] - This implies that the electric field is the negative gradient of the electric potential. 3. **Separation and Electric Field Intensity**: - The separation (d) between equipotential surfaces is inversely proportional to the electric field intensity: \[ d \propto \frac{1}{E} \] - This means that as the electric field intensity increases, the separation between equipotential surfaces decreases. 4. **Analyzing the Options**: - **Option 1**: "Closer in regions of large electric fields compared to regions of lower electric fields." - This is **correct** because a strong electric field results in closely spaced equipotential surfaces. - **Option 2**: "Will be more crowded near sharp edges of a conductor." - This is **correct** as the electric field is stronger near sharp edges, leading to closer equipotential surfaces. - **Option 3**: "Will be more crowded near regions of large charge densities." - This is also **correct** because high charge density results in a stronger electric field, thus reducing the separation between equipotential surfaces. - **Option 4**: "Will always be equally spaced." - This is **incorrect** because the spacing depends on the electric field intensity, which varies in different regions. 5. **Conclusion**: - The correct options are 1, 2, and 3. Option 4 is incorrect. ### Final Answer: - **Correct Options**: 1, 2, and 3. - **Incorrect Option**: 4.
To solve the question regarding equipotential surfaces, we need to understand the relationship between electric field intensity and the separation of these surfaces. Let's break this down step by step. ### Step-by-Step Solution: 1. **Understanding Equipotential Surfaces**: - Equipotential surfaces are surfaces where the electric potential is the same at every point. No work is done when moving a charge along an equipotential surface. 2. **Relationship Between Electric Field and Equipotential Surfaces**: ...
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