Epotential of Point Charges - Really Hard Conceptual Problem

In summary: KQ/(r2^3 - r1^3)]*{(r2^3 - r1^3)/r2 - r^2/2 - r1^3/r} = [KQ/(r2^3 - r1^3)]*[(r^3 - r1^3)/r2 - r^2/2 - r1^3/r] = [KQ/(r2^3 - r1^3)]*{(r^3 - r1^3)/r2 - r^2/2 + r1^3/r2 - r1^3/r2} = [KQ/(r2^3 - r1^3
  • #1
miguzi
7
0
A thick spherical shell of charge Q and uniform volume charge density p is bounded by radii r1 and r2, where r2 > r1. With V = 0 at infinity, find the electric potential V as a function of the distance r from the center of the distribution, considering the regions (a) r > r2, (b) r2 > r > r1

a) I got V = (kQ)/r

b) I found that p = 3Q/(4Pi(r2^3-r1^3))
using that I found that qencl = Q*(r^3-r1^3)/(r2^3-r1^3)

Then using Gauss' Law I found that E = Q/(4*PI*r^2*Eo) * ((r^3-r1^3)/(r2^3-r1^3))

Change in E potential = -integral(E)*dr lower limit r^2, upper limit r

Vr - Vr2 = -kQ/(r2^3-r1^3) * (r^2/2 - r1^3/r + r2^2/2 + r1^3/r2)

I'm stuck at this part

The answer is:
3buhz.gif

I don't how they simplified the answer to that
 

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  • #2
Should I move Vr2 to the other side?
 
  • #3
yea that's right I think, Vr2 would equal to kQ/r but I'm also stumped on how it is simplied to the final answer.
 
  • #4
First of all check the signs in the integral.
We have to find potential at distance r from the center not the potential difference between points at r and r2.
 
  • #5
All looks well down to the integral. It seems to me the integral ought to go from infinity (where you know the potential) down to r. Of course you would have to do it in two parts, from infinity to r2 and then from r2 to r. Oh, I suppose you are already taking that first part into account as the Vr2.

In the last step, Vr - Vr2, I'm having trouble with the signs on the terms in the last brackets. Surely there should be two negative terms - including the r^2/2.
 
  • #6
I think you got it.
 
  • #7
mukundpa said:
First of all check the signs in the integral.
We have to find potential at distance r from the center not the potential difference between points at r and r2.

Isn't that what I was doing? I subtract Epotential between r2 and r from the Vr2 to get Vr?

mukundpa said:
I think you got it.

I don't think so :(. I still don't know how to simplify it.

By the way reuped the pic of the answer

what I don't get is how they got (3r2^2)/2
 
  • #8
Integrating field between limits r to r2 gives potential difference between the two distances. Potential at r is the potential difference between r and infinity.
 
  • #9
My prof just posted solutions:

25gy069.jpg

I still don't get how he sub it in and simplified it
 

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  • #10
sorry i fixed the pics again.
 
  • #11
what happened to the r1^3/r2 term?
 
  • #12
Put V0 = KQ/r2 and then take KQ/(r2^3 - r1^3) common.

There are two terms r1^3/r2 with opposite sign and get canceled. The simplification is correct.
 
  • #13
I don't understand what you mean by take KQ/(r2^3 - r1^3) common.

Do you mean:

kQ/(r2^3-r1^3) * ((r2^3-r1^3)/(kQr2) - r^2/2 + r2^2/2 +r1^3/r + r1^3/r2)


I get KQ on the bottom now.
 
  • #14
NVM i got it THANK YOU!
 
  • #15
V = [KQ/r2] - [KQ/(r2^3 - r1^3)] *[r^2/2 - r2^2/2 + r1^3/r - r1^3/r2]

= [KQ/(r2^3 - r1^3)]*{[(r2^3 - r1^3)/r2 - [r^2/2 - r2^2/2 + r1^3/r - r1^3/r2]}

= [KQ/(r2^3 - r1^3)]*{r2^3/r2 - r1^3/r2 - r^2/2 + r2^2/2 - r1^3/r + r1^3/r2}
 

Related to Epotential of Point Charges - Really Hard Conceptual Problem

What is the concept of Epotential of Point Charges?

The concept of Epotential of Point Charges is a way to measure the energy associated with a system of point charges. It is a measure of the potential energy of a charged particle in an electric field.

How is Epotential of Point Charges calculated?

Epotential of Point Charges is calculated using the equation: Epotential = k * (Q1 * Q2)/r, where k is the Coulomb's constant, Q1 and Q2 are the magnitudes of the two point charges, and r is the distance between them.

What is the significance of Epotential of Point Charges in physics?

Epotential of Point Charges is a fundamental concept in understanding the behavior of electric fields and the interactions between charged particles. It helps scientists to predict the movement and behavior of charged particles in electric fields.

Can Epotential of Point Charges be negative?

Yes, Epotential of Point Charges can be negative. This indicates that the charged particles in the system have a lower potential energy when they are closer together, and the energy is released when they move further apart.

What factors affect the magnitude of Epotential of Point Charges?

The magnitude of Epotential of Point Charges is affected by the distance between the point charges, the magnitude of the charges, and the medium in which the charges are located. It is also affected by the presence of other charges in the surrounding area.

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