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 ? = 27.0. A potential difference V = 64.5 V is applied across the inner and outer shells.
(a) Determine the capacitance of the device.
nF

(b) Determine the free charge q on the inner shell.
nC

(c) Determine the charge q' induced along the surface of the inner shell.
nC

a) C = 1.065 * 10^-10 F

b) 7.775 * 10^-9

c) 7.444 * 10^-9 C

Explanation:

A spherical capacitor, with inner radius of a = 1.2 cm and outer radius  

of b = 1.7 cm is filled with a dielectric material with dielectric constant of  

K = 27 and connected to a potential difference of V = 64.5 V.  

(a) The capacitance of a filled air spherical capacitor is given by equation :

                C = 4*π*∈o*(a*b/b-a)

if the capacitor is filled with a material with dielectric constant K, we need  

to modify the capacitance as ∈o >k∈o , thus:  

                C = 4*π*∈o*(a*b/b-a)

substitute with the given values to get:  

    C = 4*π*(27)*(8.84*10^-12)[(1.2*10^-2)*(1.7*10^-2)/(1.7*10^-2)-(1.2*10^-2)*]

    C = 1.065 * 10^-10 F

(b) The charge on the capacitor is given by q = CV, substitute to get:

   q = (1.065 * 10^-10)*64.5 V

      = 7.775 * 10^-9

(c) The induced charge on the dielectric material is given by equation as:  

   q' = q(1-1/k)

  substitute with the given values to get:

    q' = (7.775 * 10^-9)*(1-1/27)

        = 7.444 * 10^-9 C

note:

calculation maybe wrong but method is correct. thanks

howdy howdy!

i'd say it would be galileo!

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement