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A very long, straight wire carries a current of 13.9 A out of the screen. An electron outside the wire is 1.17 cm to the right of the central axis of the wire and is moving with a speed of 4.25×10⁶ m/s.

a. Find the magnitude of the magnetic force on the electron if it is moving directly away from the wire (i.e., rightward).
b. Find the magnitude of the force on the electron if it is moving parallel to the wire in the direction of the current (i.e., out of the screen).
c. Find the magnitude of the force on the electron if it is moving upward.

1 Answer

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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.

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