Electric Potential from a uniformly charged sphere

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Homework Help Overview

The problem involves calculating the electric potential at specific radial distances from a uniformly charged nonconducting sphere. The sphere has a defined radius and charge, with the potential at its center set to zero. Participants are exploring how to apply electric field equations and integration to find the potential at various points both inside and outside the sphere.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to integrate the electric field to find the potential, with some questioning the assumptions about charge distribution as the radius changes. Others explore the application of Gauss's law to derive the electric field inside and outside the sphere.

Discussion Status

Some participants have provided guidance on separating the electric field expressions for inside and outside the sphere, while others express confusion about the integration process and the implications of using different approaches. There is an ongoing exploration of the correct methodology without a clear consensus on the best path forward.

Contextual Notes

Participants are grappling with the implications of integrating from infinity to a point within the sphere and the resulting terms that arise during the calculations. There is a recognition of the need for careful consideration of the electric field's behavior in different regions relative to the sphere.

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Homework Statement


A nonconducting sphere has radius R = 2.70 cm and uniformly distributed charge q = +7.00 fC. Take the electric potential at the sphere's center to be V0 = 0.

(a) What is V at radial distance r = 1.45 cm?

(b) What is V at radial distance r = R?

Homework Equations


E = Vdv
V = k (q / r)

The Attempt at a Solution


I was about to just integrate E from zero to r1 and then r2, but then I realized that as r increases, so does q so I can't just have a simple single integration. And then I didn't know what to do. Help? Thanks.
 
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Charge density in the sphere = ρ = Q/[4/3*π*R^3]
Charge enclosed in the sphere of radius r = ρ* volume of the sphere of radius r
Q' = { Q/[4/3*π*R^3]}*4/3*π*r^3
= Q*r^3/R^3
Using Gauss theorem, if the electric field E at a distance r is E, then
4πr^2E = Q/εο*r^3/R^3
Or E = 1/4πεο*Qr/R^3 = - dV/dr. Now find the integration.
 
Aaaaaahhhhhhhhhhhhh. Thank you so much! I do particularly thank you because you helped me recognize that I need to do much more variable rewriting than I've been doing.
 
i had a problem in this question,
i got E = 1/4πεο*Qr/R^3 (using gauss law)
when i applied - dV/dr. , i could not got the answer,I used the basic defination of electric potential that said bring charge from infinity to that pt , i integrated it (-E.dr) from infinity to r,as evident i gt an infinite term in numerator ,please help ?
 
I used the basic defination of electric potential that said bring charge from infinity to that pt , i integrated it (-E.dr) from infinity to r,as evident i gt an infinite term in numerator ,please help ?

To find the potential at r, you have to consider the electric field outside and inside the sphere separately.
So V(r) = -int[1/4πεο*Q/r^2*dr] from infinity to R - int[1/4πεο*Qr/R^3*dr] from R to r.
 
thanks :) but can you explain in detail that why we follow this approach and what's wrong with d other one?
 
Which one is the other approach?
You have tried to find the potential at r using the same expression for E from infinity to r. But it is wrong. Out side the sphere E = 1/4πεο*Q/r^2 and inside the sphere E = 1/4πεο*Qr/R^3. Using these expression find the integration to find the potential at r.
 

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