# Finding E field from potential

Two long conducting cylindrical shells are coaxial and have radii of 20 mm and 80 mm. The electric potential of the inner conductor, with respect to the outer conductor, is +600V.

In the situation provided, an electron is in circular motion around the inner cylinder in an orbit of 30mm radius. Find the speed of the electron in orbit.

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So where I'm stuck is mostly just in finding the E field at said point

The electron has a force radially inward putting the electron in uniform circular motion.
Therefore:

$$eE=\frac{mv^{2}}{r}$$

$$v=\sqrt{\frac{erE}{m}}$$

So, I can't seem to figure out how to find the e field around the point r =30mm

What I tried to do was the following

$$V_{a}-V_{b}=\int \vec{E} d\vec{l}$$

Then I rewrote it as

$$-\int dV =\int \vec{E} d\vec{l}$$

So $$E = -\frac{dV}{dl}$$

However I think all I've just done is derived the gradient, and I don't know how to use this without a function.

Give me a hint on how to continue my calculation or give me an easier way to calculate E

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rl.bhat
Homework Helper
Find the capacitor per unit length of the co-axial cable. Then find charge per unit length λ by using Q = C*V formula.
The electric field between the coaxial cylinder is given by
E = λ/(2*π*εο*r)

Well I can't possibly answer with that solution though. I know nothing about the length of the cylinder except that it is very long. To answer in terms of lamba would be an incomplete answer since I still have unknown variables.

Thank you rl.bhat

I took a look at the lamba again and figured out I should have simply just solved for lamba instead of q using my potential integration. Thanks!