Problem about electric potential

In summary,Can anyone help me how to solve this problem ?! I am sure that my answer is not right :I am not sure I understand your first equationSuppose that you removed the sphere and just had the two oppositely charged plates. If so how does a parallel plate capacitor get charged?
  • #1
MatinSAR
441
152
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
1.png

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

1.jpg
 
  • Like
Likes Delta2
Physics news on Phys.org
  • #2
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.
 
  • Like
Likes MatinSAR
  • #3
MatinSAR said:
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=+∞?
 
  • Like
Likes MatinSAR
  • #4
kuruman said:
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 ?!

photo_2022-04-30_08-21-50.jpg

haruspex said:
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 ?!
 
  • #5
MatinSAR said:
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?
 
  • Like
Likes MatinSAR
  • #6
haruspex said:
No. How does one find a potential difference given the electric fields?
1651292032106.png


I have said that base on this page of my book. Is it false ?!
E is 0 so DeltaV is 0.
 
  • #7
MatinSAR said:
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.
 
  • Like
Likes MatinSAR
  • #8
haruspex said:
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.
 
Last edited:
  • #9
MatinSAR said:
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.
 
  • Like
Likes MatinSAR
  • #10
haruspex said:
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.
🙏🙏
 
  • #11
MatinSAR said:
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##.
 
  • Like
Likes MatinSAR

1. What is electric potential?

Electric potential is the amount of work needed to move a unit positive charge from one point to another in an electric field. It is a scalar quantity and is measured in volts (V).

2. How is electric potential different from electric field?

Electric potential is a measure of the potential energy per unit charge at a point in an electric field, while electric field is a measure of the force per unit charge at a point in an electric field. In other words, electric potential tells us how much energy a charge would have at a certain point, while electric field tells us how much force a charge would experience at that point.

3. What is the equation for electric potential?

The equation for electric potential is V = kQ/r, where V is the electric potential, k is the Coulomb's constant (9 x 10^9 Nm^2/C^2), Q is the magnitude of the charge, and r is the distance from the charge.

4. How is electric potential related to electric potential energy?

Electric potential energy is the potential energy that a charge possesses due to its position in an electric field. It is directly proportional to electric potential, as the higher the electric potential, the higher the electric potential energy of a charge at that point.

5. What factors affect electric potential?

The factors that affect electric potential include the magnitude and location of the charge, the distance from the charge, and the medium in which the charge is located. Electric potential decreases as the distance from the charge increases, and it also varies depending on the type of material the charge is in.

Similar threads

  • Introductory Physics Homework Help
Replies
7
Views
280
Replies
22
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
250
  • Introductory Physics Homework Help
2
Replies
64
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
904
  • Introductory Physics Homework Help
Replies
9
Views
801
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
5
Views
727
  • Introductory Physics Homework Help
Replies
23
Views
257
  • Introductory Physics Homework Help
Replies
1
Views
714
Back
Top