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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:

[tex]eE=\frac{mv^{2}}{r}[/tex]

[tex]v=\sqrt{\frac{erE}{m}} [/tex]

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

[tex]V_{a}-V_{b}=\int \vec{E} d\vec{l} [/tex]

Then I rewrote it as

[tex]-\int dV =\int \vec{E} d\vec{l} [/tex]

So [tex]E = -\frac{dV}{dl} [/tex]

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