Posted by Jessica on Tuesday, April 8, 2008 at 9:47pm.
Consider a long wire where the current density is not uniform but instead increases as you approach the center of the wire, so that at a distance r from the center the current density is J(r)= I/ 2PiRr. Find the magnetic field strength both inside and outside of this wire.
I know I need to use biotsavart law, but im not sure how to do this with a non uniform density

physics  drwls, Wednesday, April 9, 2008 at 10:34am
Integrate the current from r = 0 to r = r, using the current density.
I(r) = Integral (r=0 to r) of J*2*pi*r dr
= I r/R where R is the radius of the wire
Then use Ampere's law that says the integral of H (=B/mu) around the loop equals the current flowing through the loop. The value of B will be uniform around that circular loop because of symmetry.
B(r) = mu*2*pi*(r/R)*(I/r)
= mu*2*pi*(I/R)
which is independent of r.
Outside the wire, use Ampere's law again:
B(r) = mu*2*pi(*I/r)
Answer This Question
Related Questions
 Physics  A wire of radius R carries a nonuniform current: the current density...
 physics  A wire with circular crosssection of radius 1mm carries a current of ...
 college physics  A 4m long copper wire has a diameter of 2mm and carries a ...
 physics  a Coper wire with wire with a diameter of 1.5mm is joined to an ...
 physics  The magnitude of the magnetic field produced by a long straight ...
 physics  a copper wire with a diameter of 1.5mm is joined to an aluminium wire ...
 Physics  A 550 turn solenoid is 15 cm long. The current in it is 33 A. A 3.0 cm...
 physics  A 570turn solenoid is 19cm long. The current in it is 32A . A 2.0cm ...
 physics  A 570turn solenoid is 19cm long. The current in it is 32A . A 2.0cm ...
 phys102  a copper wire has a diameter of 1.02mm,the wire carries a constant ...
More Related Questions