A long, hollow cylinder with inner radius R1R1 and outer radius R2R2 carries current along its length. The current is uniformly distributed over the cross-sectional area of the cylinder and has current density JJ. Find the magnetic-field magnitude BB as a function of the distance rr from the conductor axis for points inside the hollow interior (r

Explanation:

We shall have to apply Ampere's circuital law to find out the magnetic field asked for.

Ampere's circuital law expression is given below :

∫ B dl = μ₀ I

B is magnetic field , I is current inside the closed curve over which line integral of magnetic field is taken

If we take a point at distance r from the axis of wire  , Th magnetic field B at that point can be calculated as follows

current enclosed by the closed circle of radius r

I = cross sectional area x current density

π ( R₂² - R₁² )  x J

Applying Ampere's law

∫ B dl = μ₀ I

B  x 2π r = μ₀ x π ( R₂² - R₁² )  x J

B = μ₀ x  ( R₂² - R₁² )  x J / 2 r

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