Find magnetic field at a distance from wire

[ooohffff]

Homework Statement

A wire with radius R= .01 m carries a current with uniform density. At a distance r₁ =1.25m from the wire, the magnetic field has a magnitude of 2.55 μT. Calculate the magnitude of the magnetic field r₂=.0065m from the wire.

Homework Equations

B= (μ₀I)/ 2πr

The Attempt at a Solution

So first I did:
B₁=(μ₀I)/( 2πr₁)
Solving for I:
I = (B₁2πr₁)/μ₀
Plugging it into the B₂ equation:
B₂=(μ₀B₁2πr₁)/(2πr₂μ₀)
= (B₁r₁)/r₂
=4.9 x 10^-4 T

I'm not sure if I did this right since other people in my class got something different. Can someone corroborate this? Thanks.

 

[TSny]

Hello. Keep in mind that the equation B= (μ₀I)/ (2πr) is only valid for points outside the wire.

 

[ooohffff]

Hello. Keep in mind that the equation B= (μ₀I)/ (2πr) is only valid for points outside the wire.

Oh I see, I would have to use the equation for the magnetic field inside the wire for B₂:

B₂= (μ₀Ir₂)/ (2πR²)

Plugging I into this equation:
B₂= (μ₀B₁2πr₁r₂)/ (2πR²μ₀)
=(B₁r₁r₂)/ R²

 

[TSny]

That looks correct to me.