# There is one cylinder and one metal plate. help me calculation of electric field.

1. May 3, 2012

### india

i have to design one shielding box. in that there is cylinder having high volatage +60kev. and box having metal plate. so i have to calculate the electric field on that cylinder and then decide , what should be the distance in between plate and cylinder. i have attach the geometry on the file. please see it.

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2. May 3, 2012

### india

Could anyone help me ?

3. May 3, 2012

### Staff: Mentor

Can you use some approximation, like d>>R?
In that case, it should be possible to approximate the box as a cylinder, and calculate it like a cylindrical capacitor using Gauss' law (google should give you some ways to do this).

If not, a numerical simulation might be the easiest way to solve your problem.

4. May 3, 2012

### india

yes, thanks ... bt i think i wl get that for cylindrical capacitor. bt right now i have another design.. bt i wl try for solving it.
btw what type of numerical solution that i should use??

5. May 3, 2012

### Bob S

For a cylinder and one metal plate, the capacitance per unit length is given by Smythe Static and Dynamic Electricity 3rd edition page 78:
$$C=\frac{2\pi\epsilon}{cosh^{-1}\frac{h}{R}}$$
for cylinder of radius R with axis parallel to and at a distance h above an infinite plane. The problem of a cylinder between two conducting planes is given on page 105.

6. May 5, 2012

### Staff: Mentor

A two-dimensional grid, for example. Use your favourite tool, plug in the boundary conditions for the potential Φ (box and circle) and the Laplace equation $\nabla^2 \Phi = 0$ in the vacuum (or air, as good approximation).

In excel, the result can look like this (I did this for a cylinder over an infinite plane orthogonal to the cylinder axis, and it uses cylindrical coordinates).