Is My Equation for Finding Electric Potential in the Correct Form?

[VitaX]

Homework Statement

Homework Equations

V = (sigma)/(2*epsilon_0)*((z^2 + R^2)^(1/2) - z)

The Attempt at a Solution

This was my full equation to find the total electric potential:

V = (sigma)/(2*epsilon_0)*((z^2 + R^2)^(1/2) - z) - (sigma)/(2*epsilon_0)*((z^2 + r^2)^(1/2) - z)

But I got the answer wrong. Is this equation even correct here? I'm not seeing what I did wrong if it is the right equation to use.

 

[gneill]

I think that you may want to verify your "Relevant equation". That "-z" term looks suspicious. How did you find this equation?

 

[VitaX]

I think that you may want to verify your "Relevant equation". That "-z" term looks suspicious. How did you find this equation?

 

[gneill]

Ah. The 'z' results from the disk going from radius 0 to radius R. Your disk has a minimum radius that is not zero, so rather than a 'z' term there should be another sqrt(z² + r²) in its place, where r is the inner radius of the ring.

 

[VitaX]

Ah. The 'z' results from the disk going from radius 0 to radius R. Your disk has a minimum radius that is not zero, so rather than a 'z' term there should be another sqrt(z² + r²) in its place, where r is the inner radius of the ring.

I see, so if I do that it will complete the equation needed to solve this?

 

[gneill]

That should do it, but it might be preferable for you to do the integration and confirm where the term comes from. You might have to do something similar in an exam at some point.

 

[VitaX]

True, I know I start with dV = (1/4*pi*e_0) \integral (dQ/r)

Next step would be to say dQ = sigma*dx where sigma = Q/Area. Do I use Area = 4*pi*R^2 here? I'm a bit confused as to how about going to set this up and where the R and r come into play.

 

[gneill]

Yes, it gets a bit confusing because there are so many different r's floating around in this problem. Rename some. Call the distance from a given ring of charge to the point on the z-axis d. That takes the place of the r in the \integral (dQ/r), and is given by sqrt(z² + x²), where here x is the radius of the given differential ring of charge. The integration limits will be x = r to x = R, corresponding to the radial extremes of the disk.

Have a look http://hyperphysics.phy-astr.gsu.edu/hbase/electric/potlin.html" for the geometry and setup of the integral.