Figure shows a cylindrical wire ofdiameter a, carrying a current I. Thecurrent density which is in the directionof the central axis of the wire varies linearly with radial distance r from theaxis according to the relation J = Jr/a. Obtain the magnetic field B inside thewire at a distance r from its centre.
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Answer:
Ampere's law says that ∮B⋅dl=μ⋅I,
Here B.dl is equal to ∮B⋅dl
Here, dl is 2πr
And I=∫J.da
Finally, B×2πa/2=μ
0
×∫
0
2
a
J
0
×
a
r
×2πrdr
πaB=
a
2πμ
o
J
o
×
3
(a/2)
3
B=
12
μ
o
J
o
a
B=
12
4π×10
−7
×10
5
/4π×0.012
Putting values
B is equal to 10μT
How satisfied are
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