Define the dielectric moment is it a scalar or vector deduce an expression for the electric field at a point
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Answer:
(i) At a point P outside the spherical shell :
Let \vec E
E
be the electric field at P. The electric field through an elemental surface d\vec sd
s
is
d\phi =\vec E.d\vec sdϕ=
E
.d
s
\therefore∴ Total electric flux through the gaussian surface is
\phi = \oint _{ S }{ Eds } = E\oint _{S} ds=E\times 4\pi r^2ϕ=∮
S
Eds=E∮
S
ds=E×4πr
2
\phi =\dfrac{q}{\epsilon_{0}}ϕ=
ϵ
0
q
E\times 4\pi r^2=\dfrac{q}{\epsilon_0}E×4πr
2
=
ϵ
0
q
E=\dfrac{1}{4\pi \epsilon_0}.\dfrac{q}{r^2}E=
4πϵ
0
1
.
r
2
q
(for r>Rr>R)
(ii) At a point P inside the spherical shell:
In this case charge enclosed =0
E\times 4\pi r^2=0E×4πr
2
=0
E=0E=0 (for r<Rr<R)
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