Current carrying wire in uniform magnetic field; where is net magnetic field 0?

[mm2424]

Homework Statement

A long wire carrying 100 A is perpendicular to the magnetic field lines of a uniform magnetic field of magnitude 5.0 mT. At what distance from the wire is the net magnetic field equal to zero?

Homework Equations

B = iμ_o/2∏R

The Attempt at a Solution

I reasoned that in order for the net magnetic field at some point outside the wire to be 0, the magnetic field from the current in the wire must cancel out the uniform magnetic field (B = 5.0 mT).

So, I used B = iμ_o/2∏R

B = 5.0 x 10^-3 T = 100Aμ_o/2∏R

R = 4 mm

Is this reasoning sound?

 

[Redbelly98]

Looks good