A conducting sphere with a radius of 5 cm contains a total c

A conducting sphere with a radius of 5 cm contains a total charge of Q = +3 nC. What is the charge density ?_s on the surface of the sphere?

Hint: The electrostatic charge density inside a conducting object is zero. Therefore, all the charge must reside on the surface. For a symmetrical object like a sphere, the surface charge is uniformly distributed across the surface.

Solution

charge denisty= total charge/area

area of the sphere=4*3.14*r^2.

area of the sphere=4*3.14*(5*10^-2)^2=0.0314 metre^2.

charge denisty=3/0.0314=95.4929 nc/ metre^2.