Question

Using Gauss's law obtain the expression for the electric field due to a
uniformly charged thin spherical shell of radius R a point outside the
shell. Draw a graph showing the variation of electric field with r, for r >
R and r < R.

Answer 1

Answer:

i) At a point P outside the spherical shell :

Let

E

be the electric field at P. The electric field through an elemental surface d

s

is

dϕ=

E

.d

s

∴ Total electric flux through the gaussian surface is

ϕ=∮

S

Eds=E∮

S

ds=E×4πr

2

ϕ=

ϵ

0

q

E×4πr

2

=

ϵ

0

q

E=

4πϵ

0

1

.

r

2

q

(for r>R)

(ii) At a point P inside the spherical shell:

In this case charge enclosed =0

E×4πr

2

=0

E=0 (for r<R)