Hi, I have a problem about the capacitance of two cylinders eccentrically located one inside the other - with radii a and b resp., their centers have a distance(adsbygoogle = window.adsbygoogle || []).push({}); capart. I've tried that with the method of images, considering the eqipotential "cylinders" of a system of two infinite parallel lines of charges at distance2dapart.

The potential at any point P on the plane perpendicular to the lines is given by V = (q/(2Pi*Eps))ln(R2/R1)

where q is the charge density

R1 and R2 are the distances from line 1 and line 2 respectively, i.e. r1^2 = (x-d)^2+y^2 and r2^2 = (x+d)^2+y^2

To get eqipotential lines of the system, we equate R2/R1 to a constant k and then we get a family of circles of the plane with center at h = d(k^2+1)/(k^2-1) and radius R = [2dk/(k^2-1)] ^2

Everything seems fine. If i can figure out the two values of K corresponding to the two equipotential "circles", I will know the p.d, as well as the capacitance.

However, I have problem to solve them out without knowing the value of d.

Can someone help?

Thanks very much.

G.G

Reference:

Carl T.A. Johnk, Engineering Electromagnetic Fields and Waves 2nd Ed., pp. 222-225

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# Capacitance of eccentrical cylinders

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