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How is the electric field at the surface of a charged conductor related to the surface charge density?
- a)Proportional to each other
- b)Indirectly proportional
- c)Independent
- d)Exponential
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
How is the electric field at the surface of a charged conductor relate...
The electric field at the surface of a charged conductor is proportional to the surface charge density. The electric field is zero inside the conductor and just outside, it is normal to the surface. The contribution to the total flux comes only from its outer cross-section.
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How is the electric field at the surface of a charged conductor relate...
Understanding the Relationship
The electric field at the surface of a charged conductor is indeed directly proportional to the surface charge density. Let’s explore this connection in detail.
Electric Field and Surface Charge Density
- The electric field (E) at the surface of a conductor is determined by the surface charge density (σ).
- According to Gauss's Law, the electric field just outside the surface of a charged conductor can be expressed as:
E = σ / ε₀
Here, ε₀ is the permittivity of free space.
Proportionality Explained
- When the surface charge density increases, the charge accumulated on the conductor's surface increases.
- As a result, the electric field strength at the surface also increases.
- If σ doubles, then E also doubles.
- This indicates that E is directly proportional to σ.
Physical Interpretation
- The surface of a conductor in electrostatic equilibrium has charges uniformly distributed.
- The electric field inside the conductor is zero, while the field outside is directed perpendicular to the surface.
- This perpendicular nature ensures that any increase in surface charge density directly enhances the electric field strength.
Conclusion
- Therefore, the relationship between the electric field at the surface of a charged conductor and the surface charge density is proportional.
- This fundamental concept is crucial in understanding electrostatics, especially in the context of conductors in electric fields.
In summary, the electric field at the surface of a charged conductor is directly proportional to the surface charge density, reaffirming option 'A' as the correct answer.
The electric field at the surface of a charged conductor is indeed directly proportional to the surface charge density. Let’s explore this connection in detail.
Electric Field and Surface Charge Density
- The electric field (E) at the surface of a conductor is determined by the surface charge density (σ).
- According to Gauss's Law, the electric field just outside the surface of a charged conductor can be expressed as:
E = σ / ε₀
Here, ε₀ is the permittivity of free space.
Proportionality Explained
- When the surface charge density increases, the charge accumulated on the conductor's surface increases.
- As a result, the electric field strength at the surface also increases.
- If σ doubles, then E also doubles.
- This indicates that E is directly proportional to σ.
Physical Interpretation
- The surface of a conductor in electrostatic equilibrium has charges uniformly distributed.
- The electric field inside the conductor is zero, while the field outside is directed perpendicular to the surface.
- This perpendicular nature ensures that any increase in surface charge density directly enhances the electric field strength.
Conclusion
- Therefore, the relationship between the electric field at the surface of a charged conductor and the surface charge density is proportional.
- This fundamental concept is crucial in understanding electrostatics, especially in the context of conductors in electric fields.
In summary, the electric field at the surface of a charged conductor is directly proportional to the surface charge density, reaffirming option 'A' as the correct answer.
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How is the electric field at the surface of a charged conductor related to the surface charge density?a)Proportional to each otherb)Indirectly proportionalc)Independentd)ExponentialCorrect answer is option 'A'. Can you explain this answer?
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