Using Gauss theorem derlve an expression for electric fleld due to Length conductor
"L" of positively charge Q having constant linear charge denslty 2".
Answers
Answer:
,
Explanation:
Step 1: Statement of Gauss’s law
Gauss Law for electrostatics states that the total electric flux passing through a closed surface equals the enclosed charge in the surface divided by the permittivity of the medium.
ϕ
E
=∮(
E
⋅
dS
)=
ε
o
Q
enclosed
Step 2: Deriving an expression for electric field due to infinite plane sheet
Consider an infinite plane sheet of positive charge with charge density σ as shown in the attached figure. Electric field lines will be directed orthogonal and away from the sheet of charge. Hence, a cylindrical closed surface with its base parallel to the sheet of paper as shown in the figure is a good choice of Gaussian surface.
For the curved surface electric field is orthogonal to the surface area vector. Hence, flux linked to curved surface is zero.
ϕ
s
=0
For the plane surface, applying Gauss's Law, we get:
ϕ
s
+ϕ
b
=
ε
o
Q
enclosed
EA+EA=
ε
o
Q
enclosed
But Q=σA by definition of surface charge density
⟹
E=
2ε
o
σ
[Note : For an infinite line sheet of charge, electric filed does not depend on the distance of the point from the surface.]
Step 3: Electric flux passing through surface in given diagram
For the diagram shown in the question, enclosed charge is:
Q=2+(−1)=1 μC
Using Gauss's Law,
Electric flux through the surface is:
ϕ
E
=
ε
o
Q
=10
−6
×4π×9×10
9
≈1.13×10
5
Vm
