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5. A long cylindrical conductor of radius R carries a current I. The current density is non- uniform, and is a function of the radius according to J = br, where b is a constant. Find an expression for the magnetic field for both rR (i.e. inside and outside the conductor). Assume that R is measured from the center of the conductor.

5. A long cylindrical conductor of radius R carries a current I. The current density is non- uniform, and is a function of the radius according to J = br, where b is a constant. Find an expression for the magnetic field for both rR (i.e. inside and outside the conductor). Assume that R is measured from the center of the conductor.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Problem Statement:** A long cylindrical conductor of radius \( R \) carries a current \( I \). The current density is non-uniform, and is a function of the radius according to \( J = br \), where \( b \) is a constant. Find an expression for the magnetic field for both \( r < R \) and \( r > R \) (i.e., inside and outside the conductor). Assume that \( R \) is measured from the center of the conductor.
Transcribed Image Text:**Problem Statement:** A long cylindrical conductor of radius \( R \) carries a current \( I \). The current density is non-uniform, and is a function of the radius according to \( J = br \), where \( b \) is a constant. Find an expression for the magnetic field for both \( r < R \) and \( r > R \) (i.e., inside and outside the conductor). Assume that \( R \) is measured from the center of the conductor.
Expert Solution
Step 1

Radius of long cylindrical conductor = R

J=br, where b is a constant.

Consider a small element dr at a distance dr at a distance r frm the centre of the cable.

Current in a wire is  I

I=∫0r(2πrdr)J =∫0r(2πrbr)(dr)=2πbr33 

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