# physics

posted by .

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

• physics -

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)

## Similar Questions

1. ### Physics

A 550 turn solenoid is 15 cm long. The current in it is 33 A. A 3.0 cm long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 22 A current downward( and is connected by other wires that don't …
2. ### Physics

A wire of radius R carries a non-uniform current: the current density, j, (current per unit area) varies as a function of distance r from the central axis of the wire according to j = j0(R/r) (and j = 0 outside the wire, of course). …
3. ### phys102

a copper wire has a diameter of 1.02mm,the wire carries a constant current of 1.67A,the density of the free electrons is 8.5X10^28 e/m^3.calculate the current density and drift velocity
4. ### college physics

A 4m long copper wire has a diameter of 2mm and carries a current of 10A. Determine the ff: a. current density in the wire b. electric field c. potential difference between the ends of the wire d. resistance of the wire
5. ### physics

A 570-turn solenoid is 19cm long. The current in it is 32A . A 2.0cm -long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 27A current downward (and is connected by other wires that don't …
6. ### physics

A 570-turn solenoid is 19cm long. The current in it is 32A . A 2.0cm -long straight wire cuts through the center of the solenoid, along a diameter. This wire carries a 27A current downward (and is connected by other wires that don't …
7. ### physics

The magnitude of the magnetic field produced by a long straight current-carrying wire is: proportional to both the current in the wire and the distance from the wire proportional to the current in the wire and inversely proportional …
8. ### physics

A wire with circular cross-section of radius 1mm carries a current of The speed of the carriers inside the wire is What is the current density in the wire?
9. ### physics

a copper wire with a diameter of 1.5mm is joined to an aluminium wire which has a diameter of 2.3mm.the wire carries a current of 12A.what is the current density in each wire
10. ### physics

a Coper wire with wire with a diameter of 1.5mm is joined to an alluminium wire, which has a diameter of 2.3mm. The wire carries a current of 1.2A. What is the current density in each wire?

More Similar Questions