Final answer:
The magnetic force on an electron near a current-carrying wire varies depending on its direction of motion. If it is moving away from the wire or upward, there is a maximum force, and if moving parallel, the force is zero.
Step-by-step explanation:
The problem involves calculating the magnitude of the magnetic force on an electron when it is in the vicinity of a current-carrying wire. According to the right-hand rule and the formula F = qvB sin(θ), where q is the charge of the electron, v is its velocity, B is the magnetic field, and θ is the angle between v and B, we can find:
- a. If the electron is moving directly away from the wire, the angle θ = 90° which makes sin(θ) = 1. Therefore, the force is at maximum here, calculated by multiplying the charge of the electron (negative), its velocity, and the magnetic field around the wire, which is given by B = (μ0 * I)/(2 π * r).
- b. If the electron is moving parallel to the wire in the direction of the current, the angle θ = 0° which makes sin(θ) = 0. Therefore, the force is zero.
- c. If the electron is moving upward, the angle θ is 90° again because the electron's velocity vector is perpendicular to the magnetic field created by the wire, which results in a force which can be calculated using the same approach as in part a.