# Calculus Based Physics II

An air-ﬁlled spherical capacitor is constructed
with inner and outer shell radii of 6.4 cm and
16.1 cm, respectively.
Calculate the capacitance of the device.
The value of the Coulomb constant is
8.98755 × 10
9 N·m^2/C^2
Answer in units of pF

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1. a is inner , b is outer
a has +q
b has -q inside, +q outside

Voltage of a (integrate E to 0 at infinity
Va = q/(4 pi eo ra)

Voltage of b (same way with q)
Vb = q/(4 pi eo rb)

V = Va-Vb = (q/4 pi eo) (1/ra - 1/rb)
= (q/4 pi eo) (rb-ra)/(ra rb)

C = q/V = 4 pi eo ra rb / (rb-ra)

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