A long, cylindrical conductor of radius R carries a current I as shown in the figure below. The current density J, however, is not uniform over the cross section of the conductor but is a function of the radius according to J = 4br2, where b is a constant. a) r1 < R

A long, cylindrical conductor of radius R carries a current I as shown in the figure below. The current density J, however, is not uniform over the cross section of the conductor but is a function of the radius according to J = 4br2, where b is a constant. a) r1 < R

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter22: Magnetic Forces And Magnetic Fields

Section: Chapter Questions

Problem 24P: A current loop with magnetic dipole moment is placed in a uniform magnetic field , with its moment...

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Concept explainers

Microscopic view of current

In physics, the term current is expressed as the rate of flow of electric charges across the area per unit time (I=q/t). It propagates along in the direction of the motion of positive charges. When the current is caused by the motion of electrons, the direction of the current is opposite to the flow.

Question

a) r₁ < R

Note: See image for the original question and figure. I just need help with part a, not part b.

A long, cylindrical conductor of radius R carries a current I as shown in the figure below. The current density J, however, is not uniform over the cross-section of the
conductor but is a function of the radius according to J = 4br2, where b is a constant.
Find an expression for the magnetic field magnitude B at the following distances, measured from the axis. (Use the following variables as necessary: Ho rur, b, R.)
(a) r, < R
B =
(b) r2 > R
B =

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