At a particular instant an electron is traveling in the -z direction, with speed 2105 m/s. At the location of the electron there is a magnetic field of magnitude 0.24 T in the +z direction, due to current running in a nearby coil.What is the direction of the magnetic force on the electron? What is the magnitude of the magnetic force on the electron?
Question
At a particular instant an electron is traveling in the -z direction, with speed 2105 m/s. At the location of the electron there is a magnetic field of magnitude 0.24 T in the +z direction, due to current running in a nearby coil.What is the direction of the magnetic force on the electron? What is the magnitude of the magnetic force on the electron?
Solution
The direction of the magnetic force on the electron can be determined using the right-hand rule. However, since we are dealing with an electron, which has a negative charge, we should use the left-hand rule. Point your left thumb in the direction of the electron's velocity, which is in the -z direction, and your fingers in the direction of the magnetic field, which is in the +z direction. Your palm will then point in the direction of the force. In this case, the force is directed in the -y direction.
The magnitude of the magnetic force on the electron can be calculated using the formula F = qvBsinθ, where:
- F is the magnetic force,
- q is the charge of the electron, which is -1.6 x 10^-19 C,
- v is the speed of the electron, which is 2105 m/s,
- B is the magnetic field strength, which is 0.24 T, and
- θ is the angle between the velocity and the magnetic field, which is 180 degrees in this case.
Since the velocity and the magnetic field are in opposite directions, the sinθ is -1. Therefore, the magnitude of the force is F = -(1.6 x 10^-19 C)(2105 m/s)(0.24 T)(-1) = 8.04 x 10^-23 N.
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