Question

find the capacitance of a cylindrical and spherical capacitor
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Answer 1

Answer:

Two concentric spherical conducting shells are separated by vacuum. The inner shell has total charge +Q and outer radius rara, and outer shell has charge -Q and inner radius rbrb. Find the capacitance of the spherical capacitor.

Consider a sphere with radius r between the two spheres and concentric with them as Gaussian surface. From Gauss’s Law,

EA=qϵ0E×4πr2=Qϵ0E=Q4πϵ0r2EA=qϵ0E×4πr2=Qϵ0E=Q4πϵ0r2

To find V, we use integration on E:

E=Q4πϵ0r2–dVdr=Q4πϵ0r2–V∫0dV′=r∫0Q4πϵ0r2dr′V=Q4πϵ0rE=Q4πϵ0r2–dVdr=Q4πϵ0r2–∫0VdV′=∫0rQ4πϵ0r2dr′V=Q4πϵ0r

Hence,

Vab=Va–Vb=Q4πϵ0ra–Q4πϵ0rb=Q4πϵ0(rb–

Explanation:

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