A very long cylindrical wire of radius R carries a current $$I0$$ uniformly distributed across the $$cross-section$$ of the wire. Calculate the magnetic flux through a rectangle that has one side of length w running down the centre of the wire and another side of length R, as shown in figure.

Question

A very long cylindrical wire of radius R carries a current  $$I0$$ uniformly distributed across the $$cross-section$$ of the wire. Calculate the magnetic flux through a rectangle that has one side of length w running down the centre of the wire and another side of length R, as shown in figure.

Infinity Learn · Accepted Answer

Let us consider a rectangular strip of width dr as shown in figure.Magnetic field B at the element can be obtained from Ampere's law∮B.$$dl=$$μ$$0InetB$$×$$2$$$$π$$$$r=$$μ$$0I0$$$$π$$$$R2$$$$π$$$$r2$$         $$B=$$μ$$0I0r2$$$$π$$$$R2$$∴ dϕ$$=Bwdr$$ϕ$$=$$∫dϕ$$=$$μ$$0I0w2$$$$π$$$$R2$$∫$$0Rrdr=$$μ$$0I0w4$$π

A very long cylindrical wire of radius R carries a current $I_{0}$ uniformly distributed across the cross-section of the wire. Calculate the magnetic flux through a rectangle that has one side of length w running down the centre of the wire and another side of length R, as shown in figure.

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A very long cylindrical wire of radius R carries a current I0 uniformly distributed across the cross-section of the wire. Calculate the magnetic flux through a rectangle that has one side of length w running down the centre of the wire and another side of length R, as shown in figure.

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Ready to Test Your Skills?

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A very long cylindrical wire of radius R carries a current $I_{0}$ uniformly distributed across the cross-section of the wire. Calculate the magnetic flux through a rectangle that has one side of length w running down the centre of the wire and another side of length R, as shown in figure.