determine the electric current through cylindrical wire of length 1 and radius R current density through wire RS varying with distance from center as
j=a(r÷R)
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Answered by
0
Correct option is
C
J
0
A/3
As per the given problem, current density J is:
J=J
0
(1−
R
r
)
And area is πR
2
The current density is given by:
J=
dA
dI
dI=J(dA)
dI=J
0
(1−
R
r
)(2πrdr)(asdA=2πrdr)
dI=J
0
2π(r−
R
r
2
)dr
Integrating-
I=2πJ
0
∫
0
R
(r−
R
r
2
)dr
I=2πJ
0
[
2
r
2
−
3R
r
3
]
0
R
I=J
0
(
3
πR
2
)
I=
3
J
0
A
(since A=πR
2
)
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