Question

The magnetic force was introduced in class on March 7, 2023. In order to understand the magnetic force, we worked out two problems that are not part of any Mastering Physics homework set. For the convenience of the students, the problems were 1. Compute the electric force, magnetic force and the net force between two equal charges q>0 located at (d,0,0) and (−d,0,0). Both charges have an equal velocity of vj when the forces have to be computed. You can assume that v>0.

Answer 1

The question asks for calculations of electric and magnetic forces between two charged particles moving in a magnetic field. The magnetic force can be zero if the velocity and magnetic field are parallel, but the electric force, following Coulomb's law, still needs to be calculated. The net force is the sum of both forces and takes into consideration the direction and magnitude of each.

Step-by-step explanation:

Magnetic and Electric Forces on Moving Charges:

The problem given deals with the computation of the electric force, magnetic force, and the net force between two equally charged particles with charge q>0 moving with a velocity in a magnetic field. The electric force between two charges is governed by Coulomb's law, whereas the magnetic force depends on the charge's velocity, the strength of the magnetic field, and the angle between the velocity and the magnetic field lines. According to the Lorentz force law, the electric force is directly proportional to the charge and electric field, and the magnetic force is given by the equation F = quB sin 0, where u is the velocity of the charge, B is the magnetic field strength, and 0 is the angle between the velocity and magnetic field vectors.

To calculate the magnetic force, one must consider that the force is perpendicular to both the velocity of the charge and the magnetic field, following the right-hand rule. In the case where the velocity and the magnetic field are parallel (or anti-parallel), as mentioned in the provided information, the sine of the angle between them is zero (sin 0° = sin 180° = 0), and thus the magnetic force will also be zero. However, the electric force will still act upon the charges and needs to be computed using Coulomb's law.

Conclusion:

In summary, calculating the total force on a moving charge requires understanding both the electric and magnetic forces at play. The electric force can be found using Coulomb's law, and the magnetic force can be calculated if the velocity is not parallel to the magnetic field. The net force is the vector sum of these two forces.