A very long straight wire of radius r carries current I. The intensity of the magnetic field B at a point lying at a perpendicular distance a from the axis, with a

Question

A very long straight wire of radius r carries current I. The intensity of the magnetic field B at a point lying at a perpendicular distance a from the axis, with a<r, is ∝ .

Accepted Answer

(4) a. Given: a thick straight wire of radius r carrying I spread uniformly over its cross-section; the point lies inside it, at distance a<r from the axis. Idea: Ampere's law on a circle of radius a drawn about the axis, on which B is constant and along the circle: B×2π a=μ₀I_enc. Only part of the current threads that circle: I_enc=I×(π a²)/(π r²)=I(a²)/(r²). So B=(μ₀I)/(2π a)×(a²)/(r²)=(μ₀Ia)/(2π r²). With I and r fixed, B∝ a: the field is zero on the axis and rises to (μ₀I)/(2π r) at the surface, from where it begins to fall as 1/a.

A very long straight wire of radius r carries current I. The intensity of the magnetic field B at a point lying at a perpendicular distance a from the axis, with a<r, is ∝ ______.

Step-by-step solution

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