# Finding E field from potential

• godtripp
In summary, the two long conducting cylindrical shells are coaxial with radii of 20 mm and 80 mm. The electric potential between the inner and outer conductor is +600V. The task is to find the speed of an electron in circular motion around the inner cylinder, given that it is in an orbit of 30 mm radius. To find the electric field at this point, the conversation suggests using the formula E = -dV/dl and then solving for lambda using the equation Q = C*V.

#### 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

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!

## What is the definition of electric field?

Electric field is a physical quantity that describes the strength and direction of the force exerted on a charged particle by other charged particles in its vicinity. It is measured in units of Newtons per Coulomb (N/C).

## How is electric field related to potential?

The electric field at any point in space is equal to the negative gradient of the electric potential at that point. This means that the electric field points in the direction of decreasing potential and its magnitude is proportional to the rate of change of potential.

## What is the formula for calculating electric field from potential?

The formula for calculating electric field from potential is given by E = -∇V, where E is the electric field, V is the electric potential, and ∇ is the gradient operator.

## Can electric field be negative?

Yes, electric field can be negative. This indicates that the electric field is directed in the opposite direction of the positive charge. In other words, the electric field is pointing towards the negative charge.

## What are some real-world applications of finding electric field from potential?

Finding electric field from potential is important in understanding the behavior of charged particles in electric fields. Some real-world applications include designing electronic circuits, studying the effects of lightning strikes, and developing medical equipment such as defibrillators.