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Question : 26
Total: 26
An electric dipole of dipole moment
+ q − q 2 a
x
x > > a
→
(b) Given the electric field in the region
2 x
OR
(a) Explain, using suitable diagrams, the difference in the behaviour of a (i) conductor and (ii) dielectric in the presence of external electric field. Define the terms polarization of a dielectric and write its relation with susceptibility.
(b) A thin metallic spherical shell of radiusR Q
C + 2 Q x A
(b) Given the electric field in the region
OR
(a) Explain, using suitable diagrams, the difference in the behaviour of a (i) conductor and (ii) dielectric in the presence of external electric field. Define the terms polarization of a dielectric and write its relation with susceptibility.
(b) A thin metallic spherical shell of radius
Solution:
(a) Derivation of the expression for the Electric field E
(b) Finding the net electric flux
Electric field intensity at pointp − q
− a =
⋅
(
)
Due to charge+ q
− q =
⋅
(
)
Net Electric field at pointp
=
− q +
+ q
=
× [
−
] (
)
=
[
] (
)
=
(
)
=
⋅
For x > > a
( x 2 − a 2 ) 2 = x 4
=
⋅
(b) Only the faces perpendicular to the direction ofx
Total flux ϕ = ϕ I + ϕ I I
= ∮ I
⋅
+ ∮ I I
⋅
= 0 + 2 ( a ) ⋅ a 2
∴ ϕ = 2 a 3
ϕ =
or, 2 a 3 =
∴ q enclosed = 2 a 3 ε 0
OR
(a) Explanation of difference in behaviour of
(i) conductor
(ii) dielectric
Definition of polarization and its relation with susceptibility
(b) (i) Finding the force on the charge at centre and the charge at pointA
(ii) Finding Electric flux through the shell
(a)
In the presence of Electric field, the free charge carriers, in a conductor, the charge distribution in the conductor readjusts itself so that the net Electric field within the conductor becomes zero.
In a dielectric, the external Electric field induces a net dipole moment, by stretching/reorienting the molecules. The Electric field, due to this induced dipole moment,opposes ,but does not exactly cancel, the external Electric field.
Polarisation: Induced Dipole moment, per unit volume, is called the polarization. For Linear isotropic dielectrics having a susceptibilityχ c
P = χ e E
(b) (i) Net Force on the charge
Force on charge '2 Q A
F = E × 2 Q
=
=
ϕ =
(b) Finding the net electric flux
Electric field intensity at point
Due to charge
Net Electric field at point
(b) Only the faces perpendicular to the direction of
OR
(a) Explanation of difference in behaviour of
(i) conductor
(ii) dielectric
Definition of polarization and its relation with susceptibility
(b) (i) Finding the force on the charge at centre and the charge at point
(ii) Finding Electric flux through the shell
(a)
In the presence of Electric field, the free charge carriers, in a conductor, the charge distribution in the conductor readjusts itself so that the net Electric field within the conductor becomes zero.
In a dielectric, the external Electric field induces a net dipole moment, by stretching/reorienting the molecules. The Electric field, due to this induced dipole moment,opposes ,but does not exactly cancel, the external Electric field.
Polarisation: Induced Dipole moment, per unit volume, is called the polarization. For Linear isotropic dielectrics having a susceptibility
(b) (i) Net Force on the charge
Force on charge '
(ii) Electric flux through the shell
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