Clarification about a conductor as an equipotential

In summary, a conductor is an equipotential when it is in equilibrium, meaning that any two points within or at the surface of the conductor will have the same potential. This applies even if the conductor is in an external electric field and polarizes. The reason for this is that the field forces the electrons to move, reaching their equilibrium positions where they experience zero force. This happens quickly for a good conductor.
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Clarification about a conductor as an equipotential...

Homework Statement



This is not a specific problem, but a general question I have.

In Griffiths 2.5 (pg. 97 for Third Edition), it states that "A conductor is an equipotential. For if a and b are any two points within (or at the surface of) a give conductor, V(a)-V(b)= -∫ E dl = 0, and hence V(a) = V(b)."

Does this apply to ANY two points within the conductor? Say the conductor is in an external E field and polarizes. If I picked a point at the pole and a point in the center, would V(a) = V(b)?

The reason I am confused is because I am associating a charge density with potential... not sure if this is alright.

Thank you.
 
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Yes, a conductor is equipotential when it is in equilibrium. If you put a conductor into static electric field, its points are at different potential at the beginning, but the field forces the electrons to move, and they reach their equilibrium positions, where they experience zero force. And the time to reach the equilibrium is very short for a good conductor.

ehild
 

FAQ: Clarification about a conductor as an equipotential

1. What is a conductor?

A conductor is a material that allows electricity to flow through it easily due to its high number of free electrons. Metals, such as copper and aluminum, are common examples of conductors.

2. How does a conductor act as an equipotential?

A conductor acts as an equipotential by having a uniform electric potential throughout its surface. This means that all points on the conductor have the same electrical potential, regardless of their distance from the source of the potential.

3. Why is it important for a conductor to be an equipotential?

It is important for a conductor to be an equipotential because it prevents any potential difference from occurring within the conductor. This ensures that the flow of electricity is consistent and does not cause any damage to the conductor or any connected devices.

4. Can a conductor always be considered an equipotential?

No, a conductor cannot always be considered an equipotential. In some cases, a conductor may have a potential difference across its surface due to external factors, such as an applied voltage or uneven distribution of charge.

5. How does the shape of a conductor affect its equipotentiality?

The shape of a conductor can affect its equipotentiality by changing the distribution of charges on its surface. For example, a pointy conductor will have a higher concentration of charges at its tip, while a spherical conductor will have a more evenly distributed charge. This can lead to a difference in electric potential at different points on the surface of the conductor.

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