Find potential inside spherical shell

In summary, the potential at point A, located at a distance R/2 from the center of a conducting sphere with charge Q, due to the influence of a particle with charge q placed at a distance 2R from the sphere, can be found by summing the potentials due to the sphere and the charge. However, the potential due to the sphere is not equal to kQ/R, as it is an equipotential region and the potential at the center is not affected by the presence of the particle. The concept of image charges can be used to find the correct answer.
  • #1
utkarshakash
Gold Member
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Homework Statement


A conducting sphere of radius R has a charge Q. A particle carrying a charge q is placed a distance 2R from the sphere. Find the potential at point A located a distance R/2 from the center of the sphere on the line connecting the center of the sphere and particle q. Note that the charge distribution of the sphere is not symmetrical due to the influence of particle q


The Attempt at a Solution



The potential at point A will be equal to sum of potential due to sphere and charge 'q'.
Due to sphere, V= kQ/R
and due to charge, V= 2kq/5R

But this is not the correct answer.
 

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  • #2
utkarshakash said:
The potential at point A will be equal to sum of potential due to sphere and charge 'q'.
Due to sphere, V= kQ/R
and due to charge, V= 2kq/5R

But this is not the correct answer.

The item in red is not correct .
 
  • #3
utkarshakash said:

Homework Statement


A conducting sphere of radius R has a charge Q. A particle carrying a charge q is placed a distance 2R from the sphere. Find the potential at point A located a distance R/2 from the center of the sphere on the line connecting the center of the sphere and particle q. Note that the charge distribution of the sphere is not symmetrical due to the influence of particle q


The Attempt at a Solution



The potential at point A will be equal to sum of potential due to sphere and charge 'q'.
Due to sphere, V= kQ/R
and due to charge, V= 2kq/5R

But this is not the correct answer.

Hint:the whole sphere is an equipotential region.
 
  • #4
utkarshakash said:

Homework Statement


A conducting sphere of radius R has a charge Q. A particle carrying a charge q is placed a distance 2R from the sphere. Find the potential at point A located a distance R/2 from the center of the sphere on the line connecting the center of the sphere and particle q. Note that the charge distribution of the sphere is not symmetrical due to the influence of particle q .


The Attempt at a Solution



The potential at point A will be equal to sum of potential due to sphere and charge 'q'.
Due to sphere, V= kQ/R
and due to charge, V= 2kq/5R

But this is not the correct answer.
The reason that V= kQ/R is incorrect for the sphere is highlighted in RED above.

Use the concept of image charges .
 
  • #5
projjal said:
Hint:the whole sphere is an equipotential region.

Will the potential at centre be equal to kQ/R due to sphere?
 
  • #6
utkarshakash said:
Will the potential at centre be equal to kQ/R due to sphere?

Yeah.

You also know the potential at centre due to charge q and wid that you get the answer.
 

1. What is a spherical shell?

A spherical shell is a three-dimensional shape that is formed by the surface of a sphere. It is a hollow object with a constant thickness and a curved surface.

2. How do you find the potential inside a spherical shell?

To find the potential inside a spherical shell, you can use the formula V = kQ/r, where k is the Coulomb's constant, Q is the charge of the shell, and r is the distance from the center of the shell.

3. What factors affect the potential inside a spherical shell?

The potential inside a spherical shell is affected by the charge of the shell, the distance from the center of the shell, and the value of Coulomb's constant.

4. Can the potential inside a spherical shell be negative?

Yes, the potential inside a spherical shell can be negative if the charge of the shell is negative. It can also be negative if the distance from the center of the shell is greater than the radius of the shell.

5. How is the potential inside a spherical shell different from the potential outside?

The potential inside a spherical shell is constant and does not depend on the distance from the center, while the potential outside of the shell varies with the distance according to the inverse square law. Additionally, the potential inside the shell is affected by the charge of the shell, while the potential outside is affected by other external charges.

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