Final answer:
The magnetic force on an electron moving in the vicinity of a current-carrying wire is calculated using the magnetic force formula F = qvB sin(θ), together with Ampère's law to find the magnetic field. The direction of the force is determined by the right-hand rule and is vertically downward for a negatively charged electron.
Step-by-step explanation:
To calculate the magnetic force experienced by an electron moving in the vicinity of a long, straight wire carrying a constant current, we use the formula for the magnetic force on a charge moving in a magnetic field, which is given by:
F = qvB sin(θ)
where:
- q is the charge of the electron (-1.6 x 10-19 C)
- v is the velocity of the electron
- B is the magnetic field induced by the wire
- θ is the angle between the velocity of the electron and the direction of the magnetic field
First, we determine the magnetic field at the position of the electron using Ampère's law:
B = (μ₀I)/(2πr)
where:
- μ₀ is the permeability of free space (4π x 10-7 Tm/A)
- I is the current in the wire
- r is the distance from the wire to the electron
Once B is calculated, we can determine the force. The velocity of the electron is given by:
v = (5.00 x 104 m/s)i - (3.00 x 104 m/s)j
Since the current in the wire is in the -x direction and the magnetic field circles the wire, the magnetic field at the electron's location is into the page (or -k direction). The angle θ is perpendicular because the electron's velocity has no component in the k direction. So, we use sin(θ) = 1.
Finally, with all values known, we can calculate the magnetic force. Note that the force on the electron will be directed according to the right-hand rule, which for this scenario means it is vertically downward or in the -j direction due to the negative charge of the electron.
(Calculations are omitted since actual numerical values are not included for B and θ)