Question

Two very long, parallel wires carry electrical current in the positive z-direction. Wire #1 crosses the x-y plane at (0,3) while wire #2 crosses the x-y plane at (8, 0) (all distances in cm). Each wire carries 6 mA. (NOTE: Wire #1 is on the y axis while wire #2 is on the x axis.)

Answer 1

The magnetic field produced by Wire #1 at the location of Wire #2 is directed along the negative x-axis.

Step-by-step explanation:

To determine the direction of the magnetic field, we can apply the right-hand rule. Wire #1, carrying current in the positive z-direction and crossing the x-y plane at (0,3), produces a magnetic field at the location of Wire #2. According to the right-hand rule, if you point your thumb in the direction of the current in Wire #1 (positive z-direction) and your index finger in the direction from Wire #1 to Wire #2 (along the positive y-axis), your middle finger will point in the direction of the magnetic field at Wire #2. Thus, the magnetic field produced by Wire #1 at the location of Wire #2 is directed along the negative x-axis.

Next, we can calculate the magnetic field strength using Ampere's Law. The formula for the magnetic field (\(B\)) produced by a long straight conductor is given by
`\(B = \frac{{\mu_0 \cdot I}}{{2 \pi \cdot r}}\)`, where \(I\) is the current and \(r\) is the distance from the wire. Substituting the given values for Wire #1
`(current \(I_1 = 6 \, \text{mA}\), \(r_1 = 3 \, \text{cm}\))` and Wire #2
`(current \(I_2 = 6 \, \text{mA}\), \(r_2 = 8 \, \text{cm}\))`, we can determine the magnetic field strength at Wire #2.

In conclusion, the magnetic field produced by Wire #1 at the location of Wire #2 is directed along the negative x-axis, as determined by the right-hand rule. Calculations using Ampere's Law allow us to quantify the magnetic field strength at Wire #2 based on the given current and distances.