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 wire's cross section as J(r) = Br, where r is in meters, J is in amperes per square meter, and B = 1.70 times 10^5 A/m^3. This function applies out to the wire's 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 15.0 mum and is at a radial distance of 1.20 mm? 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

solution:

J =I/A

and in inregral form

J.dA =I equation1

A = pir2 (cross section area)

dA =2.pi.rdr

Br.(2.pi.rdr) integret it over 0 to 2*10-3 m =I

2*B*3.14(r3/3) =I

2/3*3.14(1.7*105)(2*10-3)3 =I

2847 uA =I ans

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