Question

A solid,cylindrical conductor of radius a and charge Q is coaxial with a cylindrical shell of negligible thickness, radius b > a, and charge −Q (see Figure (a)).

1. Find the capacitance of this cylindrical capacitor if its length is l.

2. Suppose we have a piece of metal sheet of length l = 5.3 cm, and width w = 10.1 cm to make a capacitor:
a. If we cut it in two equal halves and make it into a parallel capacitor with plate separation d= 0.4 cm, find the capacitance in pF.
b. If we cut it into two sections with widths 2πa and 2πb instead (a < b), and roll them up to form a cylindrical capacitor with two shells separated by thesame distance d radially, find a and b (in cm).
c. Find the capacitance of this cylindrical capacitor in pF.

Answer 1

a) C = ????(A/d) in Farads
?? is 8.8542e-12 F/m
?? is dielectric constant (vacuum = 1)
A and d are area of plate in m² and separation in m
b) b-a = d
2pia 2pib = width
solve system of equations
c) length / (2*ke*ln(b/a)) make sure to convert everything to meters

Answer 2

For Part A C=(E_0)*[((a in meters)(b in meters))/2]/(d in m) C=[(8.85X10^-12)*((0.053*0.101)/2)]/(0.004) = 5.92 X 10^12 F or 5.92 nF