00:01
In this problem, we have a uniform magnetic field in a horizontal plane and an electron traveling in that same horizontal plane in some different direction.
00:11
We want to know how many possible directions the resultant force on the electron might take.
00:21
So if we think about it, we know that the force on a moving charge through a magnetic field is equal to q times its velocity vector cross -product with the magnetic field vector.
00:37
Let's fix our magnetic field here and just say no matter what direction it is we're going to define that to be the y direction right so we know that if the velocity vector is in the x direction it has to be the result in force then has to be in the z direction if the velocity director is in the negative x direction the result and force has to be in the positive, or sorry, negative z direction.
01:17
So we know immediately that there's two possible directions that the force can take.
01:25
Likewise, we know as a property of the cross product that the cross product must always be perpendicular to a to the two vectors in the cross product.
01:36
So we know that there's no more possible directions that the force vector can be...