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Question

# A long straight wire (radius =3.0mm) carries a constant current distributed uniformly over a cross section perpendicular to the axis of the wire. If the current density is 100A/m2 . The magnitudes of the magnetic field at (a) 2.0mm from the axis of the wire and 4.0mm from the axis of the wire is

A
1.4e7T
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B
4π×108T,π2×108T
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C
4π×108T,9π2×108T
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D
π104T,9π2×108T
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Solution

## The correct option is A 1.4e−7T(a)I=JAI=J(πr2)∫B.dL=(μ0)IB(2πr)=(μ0)(J)(πr2)B=(μ0)(J)2B=(1.257e−6A2)(100Am2)(2e−3m2)2B=1.3e−7T(b)I=JAI=J(πR2)∫B.dL=(μ0)IB(2πr)=(μ0)(J)(πR2)B=(μ0)(J)(R2)2rB=(1.257e−6NA2)(100Am2)(3e−3m)2(2×4e−3m)B=1.4e−7THence, Option A is correct.

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