Electric Potential of a Sphere

In summary: I guess I forgot to put it back in.In summary, the question asks for the potential at the surface of a conducting sphere with a radius of 4.5 cm and a charge of 40 nC, surrounded by a concentric spherical conducting shell with a radius of 20 cm and a charge of -40 nC. The potential is to be calculated using the equation V = Q / (4*pi*ε0*R), where R is the distance from the center of the charge. After considering the potential at the boundary of the shell, the correct answer is 6200V.
  • #1
bmarvs04
12
0

Homework Statement



A conducting sphere 4.5 cm in radius carries 40 nC. It's surrounded by a concentric spherical conducting shell of radius 20 cm carrying -40 nC.

Find the potential at the sphere's surface, taking the zero of potential at infinity.

Homework Equations



Inside Sphere: V = Q / (4*pi*ε0*R)
Outside Sphere: V = Q / (4*pi*ε0*r)

The Attempt at a Solution



So I figured I would add these two potentials up, giving this:

V = 9*10^9 [ ( 4*10^-5 ) / .045 + ( -4*10^-5) /.2 ] = 6200000V
 
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  • #2
There is no place where the distance from the center of the charges is .045 and .2, so your calc can't be right. Also, what the heck is a nC? NanoCoulomb?

I'm confused about this one - hope LowlyPion will help us out!
I'm picturing the "sphere" inside a "shell" (hollow sphere). Are we interested in the potential at the surface of the inner sphere?

Do you know about Gauss's Law and Gaussian surfaces?
Using that, I think the E field outside the outer shell is zero, so if we were to find V by integrating E from infinity into the surface of the inner sphere, there would be no contribution from the outer charge at all. Only the inner one need be considered and only from 20 cm to 4.5 cm.
 
  • #3
Yes, nC is a nanoCoulomb, which is why my calculations were converted to Coulombs (4*10^-5). Also, I think what you're picture is correct.. and yes we are interested in the potential at the surface of the inner sphere.

Also, I probably should have said this earlier: my calculations were based off this question:

http://answers.yahoo.com/question/index?qid=20090120101033AAplj9b

Except in that example the spherical shell is non-conducting..
 
  • #4
The site posted only the numerical answer to a different question - or did I miss something?
Check that charge. 40 nC = 40 x 10^-9 C = 4 x 10^-8 C.

No doubt there is an easier way, but using V = integral of E*dr I get
V = kQ*integral (dr/r^2) from 20 cm to 4.5 cm and Q is 40 nC of the inner charge only.
V = -kQ/r evaluated at the two radii
V = -kQ(1/.045 - 1/.2)
 
  • #5
the guassian surfaces and field description sound good

so if the datum for the potential is zero at infinity, the potential will be zero at the boundary
of the shell

so how about you calculate the potential due to the sphere at the shell radius assuming there is no shell

similarly calculate the potential at the sphere surface due to the sphere assuming no shell

putting the shell in effectively shifts the potential at the shell to zero, so shift the potential at the sphere by the same amount
 
  • #6
Ha! Good catch! that ended up being the problem.. The correct answer was 6200V.. I've been doing problems with microCoulombs so I must've gotten screwed up between the two.

Thanks a bunch

And by the way, your last line of work is correct.. When I wrote it in my first post I just factored out the Q
 

What is the formula for calculating the electric potential of a sphere?

The formula for calculating the electric potential of a sphere is V = kQ/R, where V is the electric potential, k is the Coulomb's constant, Q is the charge of the sphere, and R is the radius of the sphere.

How does the electric potential of a sphere vary with distance from the center?

The electric potential of a sphere varies inversely with the distance from the center. This means that as the distance from the center increases, the electric potential decreases.

What is the significance of the electric potential of a sphere?

The electric potential of a sphere represents the amount of work required to bring a unit positive charge from infinity to a point on the surface of the sphere. It is a measure of the potential energy of the electric field surrounding the sphere.

Can the electric potential of a sphere be negative?

Yes, the electric potential of a sphere can be negative. This occurs when the sphere has a net negative charge, which creates an inward electric field that decreases the electric potential. Alternatively, the electric potential can also be negative at points outside the sphere due to the presence of other nearby charged objects.

How does the electric potential of a conducting sphere differ from that of an insulating sphere?

The electric potential of a conducting sphere is constant throughout the entire sphere, whereas the electric potential of an insulating sphere varies with distance from the center. This is because a conducting sphere allows for the free flow of electrons, while an insulating sphere does not.

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