184_notes:q_b_force

Section 20.1 in Matter and Interactions (4th edition)

We'll start thinking about the magnetic force in terms of the simplest case: a single moving charge through an external magnetic field. The source of the external magnetic field could be another moving charge, a current, a bar magnet or any combination of those. Most of the time though, we will concern ourselves with how the charge interacts with the field (whatever it may be) and we will not care as much about what produces that magnetic field. These notes will describe how we can calculate the force from the magnetic field, including the magnitude and direction of that force.

Mathematically, the magnetic force on a moving charge from an external magnetic field is given by:

FBq=qv×B

where:

  • FBq is the force on the charge by the external magnetic field (units: N).
  • q is the charge of the moving object (units: C).
  • v is the velocity that the charge is moving with (units: ms). Note that this is the velocity, not the speed, so this includes the direction.
  • B is the external magnetic field, both the magnitude and direction (units: T).

The last piece that is missing here is the cross product, which tells us about the direction of the magnetic force. Just like before when we talked about the cross product, the cross product is a way to multiply vectors that gives you a perpendicular vector as the product. In this case, this means that the magnetic force is perpendicular to the magnetic field AND to the velocity. This may seem a little counter-intuitive, but it is an important property of the magnetic field.

In terms of calculating the magnetic force, there are a couple of ways that we can go about the math. If you know the vector components of the velocity and magnetic field, one method you can use is the general cross product equation to calculate the force. This method will always work and will give you each of the components of the force, but it can be cumbersome to actually write out each component sometimes. In the other method, we can simplify the cross product to give us a magnitude of the force and we can use the Right Hand Rule to figure out the direction.

  • 184_notes/q_b_force.txt
  • Last modified: 2021/06/08 18:43
  • by bartonmo