A long, straight wire carrying a 30 A current is situated in a uniform external magnetic field of 4.0 10⁻⁴ T that is directed parallel to the current. Determine the magnitude of the resultant magnetic field at a location 2.0 cm away from the wire.

Step-by-step solution

The magnetic field produced by the long straight wire at a distance r = 2.0 cm is given by: B_ wire = ₀ I 2 r Substituting the given values: B_ wire = 4 10⁻⁷ 30 2 0.02 B_ wire = 2 10⁻⁷ 1500 = 3.0 10⁻⁴ T The direction of this magnetic field is perpendicular to the wire. The external magnetic field is parallel to the current in the wire, so it is perpendicular to the magnetic field produced by the wire. The magnitude of the external magnetic field is B_ ext = 4.0 10⁻⁴ T . Since the two magnetic fields are perpendicul