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JEE Advanced 2016 Paper 1
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© examsnet.com
Question : 5
Total: 54
An infinite line charge of uniform electric charge density
λ
lies along the axis of an electrically conducting infinite cylindrical shell of radius R. At time t = 0, the space inside the cylinder is filled with a material of permittivity
ε
and electrical conductivity
σ
. The electrical conduction in the material follows Ohm's law. Which one of the following graphs best describes the subsequent variation of the magnitude of current density j(t) at any point in the material?
Validate
Solution:
Suppose linear charge density is
λ
0
initially and
λ
at any time instant.
Electric field at distance
r
is
E
=
λ
2
π
E
r
J
=
σ
λ
2
π
E
r
d
q
d
t
=
J
(
A
)
=
−
J
σ
2
π
r
l
d
λ
l
d
t
=
−
λ
2
π
E
r
σ
2
π
r
l
λ
=
λ
0
e
−
σ
t
∕
E
Thus,
J
=
J
0
e
−
σ
t
∕
E
This is exponentially decreasing curve with value 0 at
t
=
∞
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