Asked by Jennifer
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
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
Answers
Answered by
Damon
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)
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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