Question

A neutral hollow spherical conducting shell of inner radius 1.00 cm and outer radius 3.00 cm has a +2.00-µC point charge placed at its center. Find the surface charge density how does the magnitude of the charge and radius relate? How does a -2.00µC get involved in this problem?

Answer 1

so the inner shell is closer to the +2.00μ C charge so that will attract negative charges the inner shell would have a charge of -2.00μ C

Charge density is given interns of charge and radius(surface area).

Charge density = charge/surface area

surface area of a sphere=4πr^2

so for the inner surface 4πr^2=4π(1 x 10^-2)^2=.00126 m^2

so the charge density is -2.00μ C/.00126 m^2

=-0.00159 C/m^2

so for the outer shell the charges have to equal 0 so if the inner shell has a -2.00μ C charge then the outer shell has a +2.00μ C charge

find the surface area 4πr^2=4π(3 x 10^-2)^2=0.0113 m^2

then the charge density is +2.00μ C/0.0113m^2

=+0.000177 C/m^2