The very long conducting cylinder of radius R carries a total current I parallel

Question

The very long conducting cylinder of radius R carries a total current I
parallel to the length of the cylinder. The current density is uniform
throughout the cross-sectional area of the cylinder. Point P1
is outside
the cylinder at a distance r = r1 from its center C and point P2 is inside
the cylinder at a distance r = r2 from its center C. Both points are in
the same plane, which is perpendicular to the axis of the cylinder.

b. Derive expressions for the magnitude of the magnetic field B terms of r, R, I, and fundamental
constants for the following two cases.
i. r > R (outside the cylinder) ii. 0 < r < R (inside the cylinder)

Explanation / Answer

(int B.dl = mu_0 I_{enc}) That is (B imes m{perimeter of surface} = mu_0 imes I_{ m{enclosed by that surface}}) (B_{r_1R} = mu_0 I/(2pi r_2))

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