A long, vertical wire carrying a 10 A current in the upward direction is situated in a region where a horizontal magnetic field of magnitude 2.0 10⁻³ T points from south to north. Determine the point at which the resultant magnetic field is zero.

Step-by-step solution

Let the external magnetic field be B _ ext pointing from South to North. For the resultant magnetic field to be zero, the magnetic field due to the current-carrying wire B _ wire must be equal and opposite to B _ ext . Thus, B _ wire must point from North to South. Using the right-hand thumb rule, for an upward current, the magnetic field points South on the West side of the wire. Equating the magnitudes of the magnetic fields: B_ wire = B_ ext ₀ I 2 r = 2.0 10⁻³ Substituting the given values: 4 10⁻⁷ 10 2 r = 2.0 1