# Laplacian Coaxial Cable

• jesuslovesu

## Homework Statement

If anyone could clarify this statement for me, I'm having a bit of difficulty interpreting what the heck I'm supposed to do:

"For a given potential difference V0 between the inner and outer conductors and for a given fixed value of b, determine the inner radius a for which the largest value of the electric field is a minimum."

I found the potential fairly easily using Laplace's equation
$$V(r) = \frac{V_0 ln(r/b)}{ln(a/b)}$$ (a is inner radius, b is outer)
I know that the electric field is the negative gradient of potential, but I really don't know what they are getting at.

## Answers and Replies

Homework EquationsV(r) = \frac{V_0 ln(r/b)}{ln(a/b)}E=-\nabla VThe Attempt at a SolutionI think what they are looking for is the minimum value of the largest electric field (so the maximum of the minimums). You can use the equation for the electric field to determine the electric field at various points on the surface of the inner and outer conductors. Then, you can compare the values at these points to find the point with the maximum of the minimums. This will give you the inner radius a that produces the largest value of the electric field that is also a minimum.