Question

A conducting sphere is placed within a conducting spherical shell as shown in the figure below. The conductors are in electrostatic equilibrium. The inner sphere has a radius of 1.50 cm, the inner radius of the spherical shell is 2.25 cm, and the outer radius of the shell is 2.75 cm. The inner sphere has a charge of 225 nC, and the spherical shell has zero net charge.

Answer 1

The charge on the conducting sphere is 255nC

also the net charge on the spherical shell is zero.

But to get the charge inside the conducting shell to be zero,the charge on the inner surface of the conducting shell shouldbe

-255nC. For the net charge on the spherical shell to bezero, the charge on the outer surface of the shell must be255nC

Then for the point at 1.75cm, the net charge enclosed by agaussian spherical surface having radius 1.75cm and passing throughthe point will be 255nC

Then E_at1.75cm =(9*10⁹Nm²/C²)(255*10^-9C)/(1.75*10^-2m)²

      = 7.49*10⁶N/C

For the point at 2.5cm, the net charge enclosed by agaussian spherical surface having radius 2.5cm and passing throughthe point will is 255nC - 255nC = 0C

Then E_at2.5cm = 0

And for the point at 3.4cm, the net charge enclosed by agaussian spherical surface having radius 3.4cm and passing throughthe point will be 255nC

Then E_at3.4cm =(9*10⁹Nm²/C²)(255*10^-9C)/(3.4*10^-2m)²

      = 1.98*10⁶N/C