Each of two parallel wires separated by 8.0 mm carries a 20-A current. These two currents are oppositely directed. Determine the magnitude of the magnetic field at a point that is 5.0 mm from each of the wires.
A) 2.0 mT
B) 1.6 mT
C) 1.3 mT
D) 1.8 mT
E) 1.0 mT

Question

Quizplus · Accepted Answer

By the Biot-Savart law, the magnetic field at a point due to a current carrying wire is given by:
$B = \frac{\mu_0}{4\pi} \frac{I}{r}$, where $r$ is the distance from the wire.
Since the wires are parallel and the currents are oppositely directed, the magnetic fields due to each wire will point in opposite directions and add. Thus, the total magnetic field at the point will be
$B_{total} = \frac{\mu_0}{4\pi} \frac{I}{r_1} - \frac{\mu_0}{4\pi} \frac{I}{r_2}$, where $r_1$ and $r_2$ are the distances from each wire.
Plugging in the given values, we get:
$B_{total} = \frac{\mu_0}{4\pi} \frac{20	ext{ A}}{5	ext{ mm}} - \frac{\mu_0}{4\pi} \frac{20	ext{ A}}{5	ext{ mm} + 8	ext{ mm}}$
$B_{total} \approx 1.3	ext{ mT}$, which matches choice C.

Each of Two Parallel Wires Separated by 8