A solid current carrying conductor of radius R is having current per unit area (J) as  J = α r R  where α is constant and r is distance from axis. Find magnetic field at distance x from axis of wire. Assume x > R.

(1)  µ 0 α R 2 3 x                             (2)  µ 0 α R 2 2 x
(3)  µ 0 α R 2 x                             (4) Zero

Dear Student
Using Ampere law we can writeB.ds=μoIencIn terms of current density  Ienc=J.dAB.ds=μoJ.dA =μoαrR.2πrdrFor x>RB.ds =μo0RαxR.2πxdx=μo2παx33R0R=μo2παR23B2πx=μo2παR23B=μoαR23xSo option a is right.

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