A long, straight wire carrying a current of 1.0 A is positioned horizontally within a uniform magnetic field B = 1.0 10⁻⁵ T that points vertically upward, as shown in the figure. Determine the magnitude of the resultant magnetic field at points P and Q , which are both located at a distance of 2.0 cm from the wire in the same horizontal plane.

Step-by-step solution

The magnetic field produced by a long straight current-carrying wire at a distance d is given by: B_ wire = ₀ i 2 d Given i = 1.0 A and d = 2.0 cm = 0.02 m , we get: B_ wire = 4 10⁻⁷ 1.0 2 0.02 = 10⁻⁵ T = 10 T According to the right-hand thumb rule, the direction of the magnetic field due to the wire at point P (above the wire) is outwards ( ), and at point Q (below the wire) is inwards ( ). The external uniform magnetic field is B = 1.0 10⁻⁵ T = 10 T , directed outwards ( ). At point P , both magnetic fields are i