Question

consider a uniformly charged metallic spherical shell of radius r and charge q the coulombic force experienced by the upper half of the metallic spherical shell is

Answer 1

Answer:

A thin metallic spherical sphere of radius R carries a charge +Q on its surface. A point charge +2Q is placed at a point C .

Answer 2

Answer:

The coulombic force by the upper half of the metallic spherical shell is $\bold{F_z=\frac{3Q^2}{64\pi\epsioln_0R^2} }$

Explanation:

Now the electric field inside a uniformly charged sphere is

$\vec{E}=\frac{1}{4\pi\epsilon _{0}}$

So, force per unit volume is

$\vec{F}=\rho\vec{E}=(\frac{Q}{\frac{4}{3}\piR^3 }) (\frac{Q}{\frac{4}{3}\pi\epsilon_0R^3})\vec{r}$

and force in the z-direction on $d\tau$ is

$dF_z=\frac{3}{\epsilon_0} (\frac{Q}{4\pi R^3} )^2 rcos\theta$

So, the total force on the upper half is

$F_z=\frac{3Q^2}{64\pi\epsioln_0R^2}$