Electromagnetism - Conducting Spheres and their potential

[Asrai]

Homework Statement

Two hollow concentric conducting spheres hold charges Q[1] and Q[2] as shown in the attachment.

Find the potential of each sphere, and the potential difference.

Homework Equations

Potential difference V = Phi[2] - Phi[1]

The Attempt at a Solution

I'm having some trouble with the actual question; what does it mean, the potential of each sphere? Does this mean the potential of the sphere at a distance r where r is greater than the radius? In this case I think the answer would be

Phi[1] = Q[1]/(4*Pi*Epsilon*r)

and

Phi[2] = Q[2]/(4*Pi*Epsilon*r)

I don't think this is quite correct however. Does it mean the potential *on* each sphere instead? In this case, wouldn't the potential on the inner sphere due to the bigger sphere be zero?

I'm quite confused here and any help would be appreciated!

 

[anathema]

it is important to clarify the question before attempting to provide a solution. In this case, the potential of each sphere can refer to the potential at any point on the surface of the sphere, as well as the potential at any point outside the sphere.

Assuming that the question is asking for the potential at any point on the surface of each sphere, the correct equations would be:

Phi[1] = Q[1]/(4*Pi*Epsilon*R[1])

and

Phi[2] = Q[2]/(4*Pi*Epsilon*R[2])

where R[1] and R[2] are the radii of the inner and outer spheres, respectively.

If the question is asking for the potential at any point outside the spheres, then the equations would be:

Phi[1] = Q[1]/(4*Pi*Epsilon*r[1])

and

Phi[2] = Q[2]/(4*Pi*Epsilon*r[2])

where r[1] and r[2] are the distances from the center of the spheres to the point in question.

It is important to note that the potential on the inner sphere due to the bigger sphere would not be zero, as the potential at any point on the surface of a conductor is the same. However, the potential difference between the two spheres would still be V = Phi[2] - Phi[1], as stated in the given equations.

I hope this helps clarify the question and provides a better understanding of the potential of each sphere and the potential difference between them.

 

[m2003]

I understand your confusion with the question. Let me clarify it for you. The potential of each sphere refers to the potential at any point on the surface of each sphere. This means that the potential at any point on the outer surface of the inner sphere (Phi[1]) and the potential at any point on the outer surface of the outer sphere (Phi[2]) need to be calculated.

Your equations for Phi[1] and Phi[2] are correct, assuming that r is the distance from the center of the spheres to the point where you want to calculate the potential. However, it's important to note that the potential on the inner sphere due to the bigger sphere will not be zero. This is because the charges on the outer surface of the inner sphere will experience a repulsive force from the charges on the inner surface of the outer sphere, leading to a potential difference between the two surfaces.

To calculate the potential difference between the two spheres, you can use the equation V = Phi[2] - Phi[1], where V is the potential difference. This will give you the difference in potential between any two points on the surfaces of the spheres.

I hope this clarifies the question for you. If you have any further questions, please don't hesitate to ask. As scientists, it's important to understand the concepts and equations we use to solve problems, so don't be afraid to seek clarification when needed.