Clarification about a conductor as an equipotential

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SUMMARY

A conductor is defined as an equipotential body, meaning that the electric potential is the same at any two points within or on its surface. This principle holds true even when the conductor is placed in an external electric field, as the charges within the conductor will redistribute themselves until equilibrium is reached, resulting in zero electric field inside the conductor. The time taken to achieve this equilibrium is negligible for good conductors, confirming that V(a) = V(b) for any two points within the conductor once equilibrium is established.

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  • Understanding of electric fields and potentials
  • Familiarity with electrostatics concepts
  • Knowledge of charge distribution in conductors
  • Basic principles of equilibrium in physics
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  • Study the concept of electric field lines and equipotential surfaces
  • Explore the behavior of conductors in static electric fields
  • Learn about charge density and its relation to electric potential
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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
 

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