Question

Determine the electric field and the potential at any point in space produced by a spherical

crown where the internal radius is R1 and the external one R2, with a total charge Q, for the

following cases: (a) non conducting and an uniform charge distributed throughout the volume;

and (b) metallic and on electrostatic equilibrium. Particularize the results for a solid sphere with radius R

Answer 1

Answer

a) for non conducting sphere

Inside the sphere

$E=\frac{KQr}{R^3}$

At surface

$E=\frac{KQ}{R^2}$

Outside

$E=\frac{KQ}{r^2}$

Now potential

Inside to at surface remains same

$V=\frac{KQ}{R}$

Outside

$V=\frac{KQ}{r}$

b) now for matellic sphere

Inside E=0

Surface

$E=\frac{KQ}{R^2}$

At outside

$E=\frac{KQ}{r^2}$

Potential

Inside to surface remains same

$V=\frac{KQ}{R}$

Outside

$V=\frac{KQ}{r}$