The magnitude J(r) of the current density in a certain cylindrical wire is given

Question

The magnitude J(r) of the current density in a certain cylindrical wire is given as a function of radial distance from the center of the wires cross section as J(r) = Br, where r is in meters, J is in amperes per square meter, and B = 1.90 times 105 A/m3. This function applies out to the wires radius of 2.00 mm. How much current is contained within the width of a thin ring concentric with the wire if the ring has a radial width of 10.0mu m and is at a radial distance of 1.20 mm? mu A What is the area of the ring? How can you relate the current, current density, and area when the ring is very thin?

Explanation / Answer

i = J dA = J (2 pi r dr) = B r (2 pi r dr) = 2 pi B r^2 dr = 2*3.1416*1.9e5*1.2e-3*1.2e-3*10e-6 = 17.2 uA

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