A spherical capacitor consists of an inner spherical shell of radius R1 and an outer spherical shell of radius R2, as shown above. Our goal is to calculate the capacitance of this configuration of electrodes.
To start, suppose the inner sphere has a charge +Q and the outer sphere an equal but opposite charge -Q. Find the capacitance using the following steps:
1. Use Gauss's law to find an expression for the electric field in the region between the two spheres.
2. Find an expression for the potential difference between the spheres from the electric field (you'll have to integrate the electric field from the negative electrode to the positive one).
3. Calculate the capacitance from C = Q / ΔV.
Suppose in this case that R1 = 2.00 cm and R2 = 4.30 cm. What is the value of the capacitance?
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