QUESTION 7 6 pointsSave Answer A charged sphere of radius R1

QUESTION 7 6 pointsSave Answer A charged sphere of radius R1-0.3cm and total charge Q-6 nanoCoulomb is placed at the center of a hollow spherical conducting shell (inner radius R2-1.1cm, outer radius R3-1.9 cm) which has a net charge Qshell-4.0 nanoCoulomb. (See A charged sphere o radius R1-0.3 cm and total charge Q-6 nanoCoulomb is placed a the center o a hollow spherical conducting shell inner radius R2=1.1 cm outer radius R3=1.9 cm which has a net charge Qshe F-40 nanoCoulomb See the figure, but note that the figure is not drawn to scale) Determine the resulting charge density on the inner surface of the conducting spherical shell. (Give your answer in units of nan°Coulomb / cm2)

Solution

electric field inside conductor is always zero.

and from Gauss Law,

E . A = Qin / e0

for Guassian sphere of radius r

where R2 < r < R4 , E = 0 (inside condcutor)

hence for this region , Qin = 0

Qin = charge on sphere of radius R1 + charge on inner surface of shell

Qin = Q + Qinner = 0

Qinner = - Q

surface charge density = Qinner / (4 pi R2^2 )

      = ( - 6 nC ) / (4 x pi x 1.1^2 )

     = - 0.395 n C / cm^2