Question

Two thin concentric spherical shells of radii ri and rz (ri< rz) contain uniform surface charge densities of oi and o, respectively. Determine the electric field for (a) r ri. (b) ri <r (c) r r2.
Solve a, b and c

Physics

Answer 1

two concentric spherical conducting shells of radii r1,r2 have charges q1 and q2 respectively

case (1) if r<r1 (for points inside the inner shell)

Qenclosed =0

the electric field $E*4\pi r^2=Qenclosed/\epsilon$

$E*4\pi r^2=0/\epsilon$

the electric field E=0

case 2 if r1<r<r2( for points between the shells )

Qenclosed =q1

$E*4\pi r^2=Qenclosed/\epsilon$

$E*4\pi r^2=q1/\epsilon$

$E*4\pi r^2=\sigma 1*4\pi r1^2/\epsilon$

the electric field $E=\sigma 1* r1^2/r^2\epsilon$

case 3:if r>r2 (foe points outside the shell)

Qenclosed =q1+q2

the electric field $E*4\pi r^2=Qenclosed/\epsilon$

$E*4\pi r^2=q1+q2/\epsilon$

$E*4\pi r^2=[\sigma 1*4\pi r1^2+\sigma 2*4\pi r2^2]/\epsilon$

The electric field $E=[\sigma 1* r1^2+\sigma 2* r2^2]/r^2\epsilon$