Question

Analyze and answer the following questions:

1- The magnetic force on a charged particle is perpendicular to the speed ?⃗ it moves with, so it is said that, in this case, the magnetic force does no work over the charged particle. Explain this statement.

2- Does a magnetic force acting on the moving part of a circuit do work? Justify your statement with an example and the respective equations

3- Build an example, with feasible data, of the magnetic force between two conductors that carry an electric current I. Analyze the two cases of currents in the same direction and opposite direction. Explain whether the movement of conductors can be detected at naked eye. Hint: Compare the force obtained with the gravitational force on a object of mass m.

Answer 1

(1) The magnetic force on a charged particle is perpendicular to the velocity it moves with. Since, velocity is displacement per unit time, displacement of the charged particle is parallel to velocity and also perpendicular with the magnetic field vector. Now, magnetic force is cross product of velocity vector and magnetic field vector, and hence is perpendicular to both of them. Thus, magnetic force is perpendicular to the displacement also. Now, since work done is dot product of magnetic force and displacement vectors, this dot product is equal to Fd cos (90^o) = 0, since F (magnetic force) and d (displacement) are perpendicular to each other. Hence, work done = 0. Hence, no work is done in a charge particle under the effect of a magnetic field.