Question

Proove F=qe+q(V+B)^2

Answer 1

Answer:

Explanation:

The first term is contributed by the electric field. The second term is the magnetic force and has a direction perpendicular to both the velocity and the magnetic field. The magnetic force is proportional to q and to the magnitude of the vector cross product v × B. In terms of the angle ϕ between v and B, the magnitude of the force equals qvB sin ϕ. An interesting result of the Lorentz force is the motion of a charged particle in a uniform magnetic field. If v is perpendicular to B (i.e., with the angle ϕ between v and B of 90°), the particle will follow a circular trajectory with a radius of r = mv/qB. If the angle ϕ is less than 90°, the particle orbit will be a helix with an axis parallel to the field lines. If ϕ is zero, there will be no magnetic force on the particle, which will continue to move undeflected along the field lines. Charged particle accelerators like cyclotrons make use of the fact that particles move in a circular orbit when v and B are at right angles. For each revolution, a carefully timed electric field gives the particles additional kinetic energy, which makes them travel in increasingly larger orbits. When the particles have acquired the desired energy, they are extracted and used in a number of different ways, from studies of subatomic particles to the medical treatment of cancer.