Find the capacitance of two concentric spherical metal shells,with radii a and b.
Question 2.12: Find the capacitance of two concentric spherical metal shell...
Place charge +Q on the inner sphere, and −Q on the outer one. The field between the spheres is
E=\frac{1}{4\pi \epsilon _{0}} \frac{Q}{r^{2}}\hat{r},so the potential difference between them is
V=-\int_{b}^{a}{E.dI}=-\frac{Q}{4\pi \epsilon _{0}}\int_{b}^{a}{\frac{1}{r^{2}} dr}=\frac{Q}{4\pi \epsilon _{0}}\left(\frac{1}{a}-\frac{1}{b} \right).As promised, V is proportional to Q; the capacitance is
C=\frac{Q}{V} =4\pi \epsilon _{0}\frac{ab}{\left(b-a\right) }.Related Answered Questions
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