# Lorentz Force

1. May 4, 2010

### veritaserum20

1. The problem statement, all variables and given/known data
Consider a particle of mass m that carries a charge q. Suppose that the particle is under the influence of both an electric field E and a magnetic field B so that the particle's trajectory is described by the path x(t) for a$$\leq$$t$$\leq$$b. Then the total force acting on the particle is given in mks units by the Lorentz force,

F=q(E + vxB),

where v denotes the velocity of the trajectory.

a) Use Newton's second law of motion (F=ma) to show that

ma.v = qE.v (dot products)

2. Relevant equations

3. The attempt at a solution
Tried distributing to help make sense of the problem, but didn't do much for me:
ma = qE + q(vxB)
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. May 5, 2010

### gabbagabbahey

Take the dot product of your equation with v and use an appropriate vector identity to simplify it.