An electron moving with velocity V along the axis approaches a circula...
Magnetic Force on an Electron Approaching a Circular Current Carrying Loop
Introduction
When an electron moves with a velocity V towards a circular current carrying loop, it experiences a magnetic force due to the magnetic field produced by the loop. This force is perpendicular to both the velocity of the electron and the direction of the magnetic field.
Magnitude of Magnetic Force
The magnitude of the magnetic force on the electron can be calculated using the formula:
F = qvB sinθ
where F is the magnetic force, q is the charge of the electron, v is the velocity of the electron, B is the magnetic field, and θ is the angle between the velocity of the electron and the magnetic field.
In this case, the magnetic field produced by the circular current carrying loop is perpendicular to the axis along which the electron is moving. Therefore, θ = 90°, and sinθ = 1.
Thus, the magnitude of the magnetic force on the electron can be simplified to:
F = qvB
Explanation
The magnetic force on the electron is caused by the interaction between the magnetic field produced by the circular current carrying loop and the motion of the electron. When the electron moves towards the loop, it generates a magnetic field of its own, which interacts with the magnetic field of the loop to produce a force on the electron.
The direction of the magnetic force is given by the right-hand rule, which states that if the thumb of the right hand points in the direction of the velocity of the electron, and the fingers point in the direction of the magnetic field, then the palm of the hand gives the direction of the magnetic force.
In this case, since the electron is moving towards the loop along the axis, the direction of the velocity of the electron is along the axis, and the direction of the magnetic field produced by the loop is perpendicular to the axis. Therefore, the magnetic force on the electron is perpendicular to both the velocity of the electron and the direction of the magnetic field, and is directed towards the center of the loop.
Conclusion
In conclusion, when an electron moves with a velocity V towards a circular current carrying loop, it experiences a magnetic force towards the center of the loop. The magnitude of this force can be calculated using the formula F = qvB, where q is the charge of the electron, v is the velocity of the electron, and B is the magnetic field produced by the loop.