a) In this problem to calculate the capacitance one needs to calculte electric field every where due to cylindrical symmetry and electrostatic potential.
Applying Gauss's law to the above cylindrical capacitor problem
Where
The capacitance is given by
Substituting the above all known in the third equation gives
Where b = 27 cm, a = 20 cm, L = 36 cm. Capacitor is filled with tio2 so instead of epsilon _0 one has to put relative permitivitty. where is 78 and = 8.854x10^-12 F/m
Substituting above all gives.
C=5.206 x 10^-9 Farad
I have built a cavity resonator consisting of two concentric conducting cylinders having radii of 20...
2) Consider a coaxial capacitor with two concentric metal cylinders of radii a and b (a < b), filled with a dielectric material whose permittivity e varies linearly from ea at r = a to Ep at r = b. a. Find the capacitance per unit length. b. Find the numerical value of the capacitance if the radii are 2 mm and 6 mm and the relative dielectric constant varies from 2.25 to 8.5, respectively.
The space between two concentric conducting spherical shells of radii b = 2.20 cm and a = 1.20 cm is filled with a substance of dielectric constant κ = 24.2. A potential difference V = 50.0 V is applied across the inner and outer shells. Determine (a) the capacitance of the device, (b) the free charge q on the inner shell, and (c) the charge q induced along the surface of the inner shell.
The space between two concentric conducting spherical shells of radii b = 1.70 cm and a = 1.20 cm is filled with a substance of dielectric constant κ = 20.5. A potential difference V = 62.0 V is applied across the inner and outer shells. (a) Determine the capacitance of the device. (b) Determine the free charge q on the inner shell. (c) Determine the charge q' induced along the surface of the inner shell.
Tipler6 24.P.045. Three concentric, thin, long conducting cylindrical shells have radii of 2.00 mm, 3.00 mm, and 8.00 mm. The space between the shells is filled with air. The innermost and outermost cylinders are connected at one end by a conducting wire. Find the capacitance per unit length of this configuration. pF/m
Two conducting concentric spheres (shells)have radii R1 = 10 cm and R2 = 20 cm. Both spheres are charged to Q = +20 C. Find: (i) The electric field within the spheres and out of the external sphere. (ii) The potential difference between the spheres. (iii) The electric field profile if the spheres are connected by a thin conducting wire.