How to Find E Field from Potential in Coaxial Cylinders?

[godtripp]

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

 

[rl.bhat]

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)

 

[godtripp]

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.

 

[godtripp]

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!