Two long parallel wires 10 cm apart carry currents of 4.2 A and 8.7 A in the same direction.Is there any point between the two wires where the magnetic field is zero?

Question

Quizplus · Accepted Answer

The magnetic field due to the 4.2-A wire at a distance x from it is given by B1 = μ0*4.2/(2πx), where μ0 is the permeability of free space. The magnetic field due to the 8.7-A wire at the same distance is B2 = μ0*8.7/(2π(0.1-x)). The total magnetic field at that point is the vector sum of B1 and B2. We want to find the distance x where the total magnetic field is zero. This requires that B1 and B2 have equal magnitudes and opposite directions, or B1 = -B2. Solving for x gives x = 0.033 m or 3.3 cm, which is option C.

Two Long Parallel Wires 10 Cm Apart Carry Currents of 4.2