Question

A long, cylindrical wire of radius R has a current density J(r) = J_o(1 – r²/R²) for distances where r < R and J(r) = 0 for r < R where r is the distance from the center of the wire’s axis.

1. Find the magnetic field strength inside (r < R) and outside (r > R) the wire.
2. Sketch the magnetic field strength as a function of distance r from r = 0 to r = 2R.
3. Find the location where the magnetic field strength is a maximum AND the value for B at that location.

Please be as detailed as possible when explaining the steps.

Answer 1

The magnetic field

According to Ampere Law 82R (inside) & Bide = lo s soda B & de = uo fto (1-22) (217846) r B (2018) = 460 Jo(212) 61-72.) rad B = Mo Jo (22 8 B = Mo Jo [ r rel and r>R (outside) & B de = Mo J Jo ( 1-8 2 / 2 Trar 2 Trax

CC 2.ra ) = Jo (2Г) ( 4-82 / о B = Mo Jo / R — P 1e2 / а — до 15 — — в — Л. То 2R

000 0 0 0 0 0 0 for maximum a (8-83 ) = 0 1-382 -0 2 R2 r2=282 2 R2 Ir=1 ₃ R Bmax = Mo Jo J R ( 1- 26 ) To 1 2 3R ( 2 ) Bmax = toJo R 1 J ² ) fB max = 1 2 3 Mosor = Molo I - 13- 15 pages