Electric potential inside conductor derivation

In summary, the conversation discusses how to derive the electric field inside a charged spherical conductor, with a given potential formula. The speaker starts by finding the derivative of the formula for the potential outside the conductor, but realizes that Ke and Q are constants. They then substitute the derivative into the first formula to solve for the potential inside the sphere, which results in a constant value. However, when submitting the answer, it requires a numerical value. The speaker realizes that this is because the E field is dV/dr, whereas V is constant inside the conductor, resulting in a zero value. The speaker also mentions using Gauss's law and intuition to confirm this. The conversation ends with a discussion on the consistency of the electric field and potential inside,
  • #1
bemigh
30
0
Hey, i have this question:
The electric potential inside a charged spherical conductor of radius R is given by V = keQ/R and outside the conductor is given by V = keQ/r. Using E=-dV/dr, derive the electric field inside this charge distribution.

Alright, so I started to find the derivative of the formula for the potential outside the conductor, however Ke, and Q are constants. Therefore E=-KeQ. Subbing into the first formula, to solve for the potential inside the sphere, i got E= -V/R. Sounds good?
well, when i submit my answer, it says it needs a numerical answer, did i go wrong somewhere?
Brent
 
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  • #2
R is constant and r is variable...
the E field is dV/dr whereas V is constant inside the conductor, therefore, the answer is zero...
 
  • #3
Convince yourself of the physical implications of what vincentchan said, by using Gauss's law and intuition.

(a) what should the electric field inside and outside such a body be?
(b) what should the electric potential inside, on the surface and outside such a body be?

are (a) and (b) mutually consistent? If so, why? And if not, why not (in your answer that is)?
 

1. What is the purpose of deriving the electric potential inside a conductor?

The purpose of deriving the electric potential inside a conductor is to understand the behavior of electric charges within a conducting material. This allows us to predict how the charges will distribute themselves and how the electric field will be affected within the conductor.

2. How is the electric potential inside a conductor derived?

The electric potential inside a conductor is derived using the Laplace's equation, which describes the relationship between the electric potential and the electric field. By solving this equation, we can obtain the electric potential at any point inside the conductor.

3. What are the key assumptions made when deriving the electric potential inside a conductor?

The key assumptions made when deriving the electric potential inside a conductor are:

  • The conductor is in electrostatic equilibrium.
  • The conductor is a perfect conductor, meaning it has zero resistance and can distribute charges evenly.
  • The electric field inside the conductor is zero.
  • The conductor is a closed surface, meaning there are no holes or gaps in its structure.

4. How does the shape and size of a conductor affect the electric potential inside?

The shape and size of a conductor can affect the electric potential inside by changing the distribution of charges. For example, a smaller conductor will have a higher charge density, resulting in a higher electric potential. The shape of the conductor can also affect the electric potential by influencing the electric field lines and the distance between charges.

5. Can the electric potential inside a conductor be negative?

Yes, the electric potential inside a conductor can be negative. This occurs when there is a negatively charged object inside the conductor, causing the charges to redistribute and create a negative potential at certain points within the conductor. However, the overall electric potential inside the conductor will be zero due to the electrostatic equilibrium condition.

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