E6chalsoln

# E6chalsoln - Phy sics 7B WS E6 Challenge Solution(rev 1.0...

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Physics 7B WS E6 Challenge Solution (rev. 1.0) Page 1 E-6 Challenge Problem Force on a Dielectric in a Cylindrical Capacitor Consider a cylindrical capacitor with inner radius a, outer radius b, and length l (ignore any fringing effects). a) What is the capacitance of this capacitor? To find the capacitance, put a charge +q on the inner cylinder and a charge -q on the outer cylinder. We will assume that the length, l , is much bigger than a or b, so we can ignore fringing effects when we find the electric field. To find the electric field, assume that the cylinders are infinitely long with a charge per unit length λ = ± q/ l . Use a gaussian cylinder of length l and radius r (a < r < b). By the cylindrical symmetry, the electric field only depends on the radius r and only points in the radial direction. Therefore, the flux through the cylinder is Φ = 2 π r l E(r). The enclosed charge is just λ l = q, so r E ( r ) = q 2 "# 0 r l ! r To find the potential difference between the cylinders, integrate the electric field over the path

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