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

answer: the correct answer is 1.

explanation: there are various process in which a radioactive nuclei decays:

1) alpha decay: in this process, a heavier nuclei decays into lighter nuclei by releasing alpha particle. the mass number is reduced by 4 units.

2) electron capture: in this decay process, a parent nuclei absorbs an electron and gets converted into a neutron. simply, a proton and an electron combines together to form a neutron. mass number does not change in this process.

3) gamma ray emission: it is a decay process in which an unstable nuclei gives excess energy by a spontaneous electromagnetic process. this decay releases . this process does not change the mass number.

4) positron emission: it is a type of decay process, in which a proton gets converted to neutron and an electron neutrino. this is also known as -decay. in this the mass number remains same.

from the above information, we see that only alpha-decay is producing a change in the mass number of the nucleus.

true is the correct answer

hope i