What is the Electric Field at a Small Distance from a Charged Ring?

In summary, the conversation discusses finding the electric field at a small distance r away from the center of a ring with a distributed charge. The solution involves integrating the electric field contributions from each part of the ring and may be easier to work with the potential instead of the field. Using this method, the answer is found to be Qr/8πε0a^3.
  • #1
thepopasmurf
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Homework Statement



I have a ring, radius a, with a charge distributed evenly around it. Using a gaussian cylinder of radius r, r<<a (or otherwise). Find the electric field at at small distance r away from the centre of the ring, r is in the plane of the ring.

I know that the answer is

[tex]\frac{Qr}{8\pi\epsilon_0 a^3}[/tex]



Homework Equations



[tex]\int E\cdot ds = Q/\epsilon_0[/tex]


The Attempt at a Solution



I can't get started since I find that the charge enclosed is 0

Thanks
 
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  • #2
Don't try to use Gauss's law. (What would be your Gaussian surface? Is the field uniform across it?) Instead, integrate the field contributions from each part of the ring. (It might prove easier to work with the potential instead of the field.)
 

FAQ: What is the Electric Field at a Small Distance from a Charged Ring?

What is the formula for calculating the electric field within a ring?

The formula for calculating the electric field within a ring is E = (kqz)/((z^2 + R^2)^(3/2)), where E is the electric field, k is the Coulomb constant, q is the charge of the ring, z is the distance from the center of the ring, and R is the radius of the ring.

How does the electric field within a ring vary with distance from the center of the ring?

The electric field within a ring varies inversely with the square of the distance from the center of the ring. This means that as the distance from the center increases, the electric field decreases.

Can the electric field within a ring be negative?

Yes, the electric field within a ring can be negative. This occurs when the charge of the ring is negative and the distance from the center is larger than the radius of the ring.

How does the electric field within a ring change if the ring is charged with a different amount of charge?

The electric field within a ring is directly proportional to the amount of charge on the ring. This means that if the charge is doubled, the electric field will also double. If the charge is halved, the electric field will also be halved.

Is the electric field within a ring affected by the presence of other charges?

Yes, the electric field within a ring can be affected by the presence of other charges. If there are other charges nearby, they can create an external electric field that can interact with the electric field within the ring.

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