Problem about electric potential

[MatinSAR]

Homework Statement

A spherical shell with radius R and surface charge density σ is located between two infinite plates with surface charge density σ and -σ . The electric potential at x=∞ is zero. find the electric potential at the center of the sphere and x=-∞

Relevant Equations

Electric potential equations.
V=kq/r
dV=kdq/r

Can anyone help me how to solve this problem ?! I am sure that my answer is not right :

 

[kuruman]

I am not sure I understand your first equation $$V=V_{\sigma}+\cancel{V_{\sigma}}+\cancel{V_{-\sigma}}=V_{\sigma}.$$ Suppose that you removed the sphere and just had the two oppositely charged plates. Would you say that the potential between them is zero because $$V=\cancel{V_{\sigma}}+\cancel{V_{-\sigma}}=0~?$$If so how does a parallel plate capacitor get charged?

Also $V=\frac{kQ}{r}$ is the potential from a single point charge. Here you have a whole lot of charges distributed over three surfaces so this equation does not buy you much. I think it is safe to assume that the surfaces are not conducting and correctly superimpose potentials from two planes and a sphere.

 

[haruspex]

Homework Statement:: A spherical shell with radius R and surface charge density σ is located between two infinite plates with surface charge density σ and -σ . The electric potential at x=∞ is zero. find the electric potential at the center of the sphere and x=-∞

View attachment 300780

Care is needed wrt the infinities. Potentials in general have no fixed zero: you can define it to be zero at some point, and the potential at all other points is relative to that. Taking it to be zero at infinity is just a convention used in most electrostatics questions.
Here, note that it specifies it to be zero at x=∞ but implies it is not zero at x=-∞. How can this be? The key is the other infinity in the question: the extent of the plates.

Start by considering the field due just to the pair of plates. What is it between the plates? What is it outside them? What does that tell you about the p.d. they will create between x=-∞ and x=+∞?

 

[MatinSAR]

I am not sure I understand your first equation

Thank you!
I don't know why some professors at university give students hardest questions to solve.
I couldn't even find similar question in Halliday/serway/university physics/… books …

Now I think electric potential due to spherical shell inside it is 0 because we don't have electric field inside it.
Is it right ?!

And I think electric potential due to those infinite planes is Ed. (E is electric field inside of plates and d is distance between plates.)
Is it right ?!

Start by considering the field due just to the pair of plates. What is it between the plates? What is it outside them? What does that tell you about the p.d. they will create between x=-∞ and x=+∞?

Thank you …
Can I say p.d. is zero because there is no electric filed outside ?!
I mean p.d. between x=-∞ and x=+∞ is zero so at x=-∞ electric potential is 0 .
Is it right ?!

 

[haruspex]

Can I say p.d. is zero because there is no electric filed outside ?!

No. How does one find a potential difference given the electric fields?

 

[MatinSAR]

No. How does one find a potential difference given the electric fields?

I have said that base on this page of my book. Is it false ?!
E is 0 so DeltaV is 0.

 

[haruspex]

I have said that base on this page of my book. Is it false ?!
E is 0 so DeltaV is 0.

You have to do the integral all the way from x=-∞ to x=+∞. The field is not zero for some of that.

 

[MatinSAR]

You have to do the integral all the way from x=-∞ to x=+∞. The field is not zero for some of that.

So now I am 90% sure that electric potential at x=-∞ is -Ed. (E is electric field inside of plates and d is distance between plates.)

I'm sorry I said so much wrong.

 

[haruspex]

electric potential at x=-∞ is -Ed. (E is electric field inside of plates and d is distance between plates.)

Yes, that is how to find the potential at x=-∞ due to the charges on the plates. Now you have to add that due to the sphere. The same method can be used: integrate the field due to the sphere between x=-∞ and x=+∞ (which is trivial).
Then figure out the potential at x=0.

 

[MatinSAR]

Yes, that is how to find the potential at x=-∞ due to the charges on the plates. Now you have to add that due to the sphere. The same method can be used: integrate the field due to the sphere between x=-∞ and x=+∞ (which is trivial).
Then figure out the potential at x=0.

Well based on your tips final answer for electric potential at x=-∞ is - Ed ?! Am I right?!
Thank you so much for your help.

 

[haruspex]

Well based on your tips final answer for electric potential at x=-∞ is - Ed ?! Am I right?!
Thank you so much for your help.

Yes, but you need to express it in terms of the given variables $R, \sigma$.