Question

1. Find the electric field magnitude midway through the nonconducting wall of a thick-walled pipe of infinite length with inner radius w, outer radius 3w, and a uniform volumetric charge density ρ. Answer in terms of the permittivity.

2. Find the electric field strength due to two completely hollow, concentric spherical shells made of metal. The inner shell has a radius w and carries a uniform surface charge density -σ. The outer has radius 2w and uniform charge density +4σ. Answer in terms of epsilon, and find the result first at a distance r from the center (w<r<2w) and then at r' from the center (r'>2w). You may find the answers interesting.

Answer 1

(a)

Given,

The inner radius of the non-conducting wall of a thick-walled pipe is w & its outer radius is 3w.

Let the charge be q & uniform charge density be .

= charge(q)/volume(v) = q/ (4/3 r³) = q/ {4/3 (w+3w)³}

q = . {4/3 (w+3w)³} ------------------------------------(1)

Now, to find the electric field magnitude midway through the nonconducting wall of a thick-walled pipe of infinite length.

Electric field,E =

     . ² =   _. ()²

_. [ Here putting the value of q from the euation (1)]

Thus electric field, E =

(b)

Given there is two completely hollow concentric spherical shells made of metal, inner radius w and uniform surface charge density be - .

Outer spherical shell has radius 2w and uniform charge density be +4 .

Surface charge density of inner shell, - = charge(q)/ surface area(s)

-= q /(4w²) q = (-).(4w²)

Surface charge density of outer shell, 4= charge(q)/ surface area(s)

4 = q /{4(2w)²} q = (4).{4(2w)²}

Electric field strength,E

=

= .

= ----------------------------------------------(2)

Electric field strength at outer shell, E

=

=

= -----------------------------------------(3)

now dding equation (2) & (3), we get electric field strength,E be

=

= [ Answer]