Final answer:
To calculate the magnetic force on an electron near a current-carrying wire, you use the equation F = qvB sin(\theta), taking the magnetic field around the wire into account, which is calculated using B = \(\frac{\mu_0 I}{2 \pi r}\). The direction of the force is opposite for an electron due to its negative charge.
Step-by-step explanation:
To find the magnetic force experienced by an electron moving in the vicinity of a long, straight wire carrying a current, we use the equation for the magnetic force on a moving charge: F = qvB sin(\theta), where q is the charge of the electron, v is its velocity, B is the magnetic field strength at the location of the electron, and \(\theta\) is the angle between the velocity vector and the direction of the magnetic field.
The magnetic field around a long straight wire is given by B = \(\frac{\mu_0 I}{2 \pi r}\), where \(\mu_0\) is the permeability of free space, I is the current through the wire, and r is the distance from the wire to the point of interest. The direction of the magnetic field can be determined using the right-hand rule.
Given that the electron is at point (0, 0.200 m, 0) and has a velocity v = (5.00 \(\times\) 10^4 m/s)i^ - (3.00 \(\times\) 10^4 m/s)j^, and the current in the wire is 8.60 A in the -x-direction, the magnetic field at the electron's location can be calculated. Then, the magnetic force on the electron is F = qvB sin(\theta). Since the electron is negatively charged, the direction of the force will be opposite to that predicted by the right-hand rule for a positive charge.