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A force F, acting on an electric charge q, in presence of an electro- .magnetic field, moves the charge parallel to the magnetic field with velocity v. Then F is equal to (where B and B are electric field and magnetic field respectively)
Explanation
The total force on a charge q moving in an electromagnetic field is given by the Lorentz force law: F = q(E + v × B) [1]. This force consists of an electric component (qE) and a magnetic component (q(v × B)). The magnitude of the magnetic force is F_m = qvB sinθ, where θ is the angle between the velocity vector v and the magnetic field B. According to the problem, the charge moves parallel to the magnetic field, meaning θ = 0°. Since sin(0°) = 0, the magnetic force component becomes zero. Consequently, the only force acting on the charge is the electric force, F = qE. The electric force is independent of the particle's velocity and remains parallel to the electric field.
Sources
- [1] https://www.sciencedirect.com/topics/physics-and-astronomy/lorentz-force
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