# Equation for magnetic field

1. Dec 1, 2008

### pyroknife

Right now I'm looking at this equation for magnetic field force where F=BqVsinΘ where B is magnetic field, q is charge of particle, and V is velocity. However I've seen from some sites that F does not include sinΘ so I was confused on whether which one is right. And also what is Θ in respect to. Is it the angle of the particle direction to the magnetic field?

2. Dec 1, 2008

### buffordboy23

This is the vector form of the equation for the force on a charged-particle with some velocity in a magnetic field:

$$\vec{F} = q\vec{v}\times\vec{B}$$

If your given the velocity and the magnetic field in vector form, i.e. $$\vec{v} = \left(v_{x}\right)\hat{x} + \left(v_{y}\right)\hat{y} + \left(v_{z}\right)\hat{z}$$, then you can determine the force vector by taking the cross-product. Clear?

Using just magnitudes of the quantities gives the second-form:

$$F = qvBsin\theta$$

where $$\theta$$ is the angle between the velocity, v, and the magnetic field B. This form is used quite often when v and B are constants. Now, if $$\theta = \pi/2$$ then the sine term has value 1, so when you do not see the sine term this is what you should assume. Clear?