The current density across a cylindrical conductor of radius 1.20 mm varies in m

Question

The current density across a cylindrical conductor of radius 1.20 mm varies in magnitude according to the equation J = (0.250 A/mm2 )(1-(r/1.20 mm )) where r is the distance from the central axis. Thus, the current density is a maximum of 0.250 A/mm2 at the axis (r=0) and decreases linearly to zero at the surface (r=1.20 mm ).

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Part A

Calculate the current in the wire.

---------------------------A

Part B

Suppose that, instead of the case described in the introduction, the current density is a maximum of 0.250 A/mm2 at the cylinder's surface and decreases linearly to zero at the axis, i.e. J = (0.250 A/mm2 )(r/1.20 mm ). Calculate the current in the wire.

----------------------------A

Explanation / Answer

J = I/A

I = J*2pi*r*dr from 0 to 1.2

I = (0.250 A/mm^2) 2pi * r (1-r/1.20)dr from 0 to 1.2

I = 0.5*pi*(r-r^2/1.20)dr

I = 0.5*pi(r^2/2 - r^3/3.60 ) from o tp 1.2

I = 0.5*pi*(0.72 - 0.48 )

I = 0.3768 A

part b )

I = int J.2pi r.dr

I = 0.5*pi r^2/1.20 dr from 0 to 1.2

I = 0.5 * pi * r^3/3.60 from 0 to 1.2

I = 0.7536 A

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