on what factors do the derivation of particle in an electromagnetic field depends upon?
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Answers
Answer:
On what factors does the amount of deviation of the particles from their path in the presence of electric and magnetic field depend?
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There is a formula describing this phenomena which elucidates these factors.
The force acting on a particle in an electric and magnetic field is given by
F = qv x B + qE
The first term is the force from the magnetic field which is dependent on the charge, q, and the velocity, v crossed with the magnetic field vector B. This force is perpendicular to both the direction of motion and the magnetic field. The other force from the electric field is in the direction of the electric field and dependent as well on the charge of the particle.
This formula can be broken down further by making a differential equation and dividing everything by the mass of the particle.
dx^2/d^2t = (qv_x x B_x + qE_x)/m
You then substitute dx/dt for velocity and solve the differential equation for x as a function of time which I won't be doing. Also you would want to put the electric and magnetic field terms in an expression that shows how they vary over space. Note that this is only for one dimensional motion. In reality we would be analyzing the motion in three dimensions so there would be a set of 3 differential equations in the x, y, and z directions
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