## Sunday, June 6, 2010

### Irodov Problem 3.43

From Problem 3.9 Eqn 4, we already know that the field due to a ring of radius R with charge q at a distance x along its axis is given by,

Hence the electric field due to the two rings is given by,

For , we can use Taylor's series with l as the variable around zero and approximate the electric field as,

When the electric field becomes,

We also know that the potential due to a ring of radius R with charge q at a distance x along the axis is given by,

Hence, the potential due to the two rings is given by,

For , we can use Taylor's series with l as the variable around zero and approximate the potential as,

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