Asked by Jessica
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 biot-savart law, but im not sure how to do this with a non uniform density
I know I need to use biot-savart law, but im not sure how to do this with a non uniform density
Answers
Answered by
drwls
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)
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)
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.