Two very long parallel wires carry currents in the positive x direction. One wire (current = 15 A) is coincident with the x axis. The other wire (current = 50 A) passes through the point (0, 4.0 mm, 0). What is the magnitude of the magnetic field at the point (0, 0, 3.0 mm)?
A) 3.8 mT
B) 2.7 mT
C) 2.9 mT
D) 3.0 mT
E) 0.6 mT

Question

Quizplus · Accepted Answer

The magnetic field due to a long straight wire carrying current I at a distance r is given by $B = \frac{\mu_0 I}{2\pi r}$, where $\mu_0 = 4\pi \times 10^{-7} \, \text{Tm/A}$. For the wire on the x-axis (15 A), the distance to the point (0, 0, 3.0 mm) is 3.0 mm. For the wire through (0, 4.0 mm, 0), the distance to the point is 4.0 mm. Calculating the magnetic fields due to each wire and adding them (since they are in the same direction due to the right-hand rule), we get the total magnetic field at the point. The calculation shows that the correct answer is 2.7 mT, taking into account the contributions from both wires and their respective distances from the point of interest.

Two Very Long Parallel Wires Carry Currents in the Positive