# Calculate the force on a particle from magnetic field of infinite wire

1. Feb 20, 2013

### eviljay

1. The problem statement, all variables and given/known data
Problem: Determine an expression for the magnitude of the magnetic force on a charged particle moving near an infinitely long wire, carrying a current i.
• Particle with charge q
• Magnitude of the particles velocity = |v|
• Magnetic field strength = B
• Current = i

2. Relevant equations
B can be calculated with:
$B=\frac{μ_{0}i}{2\pi{r}}$

Magnitude of force can be calculated with:
$F=q*v*b*sin(θ)$ (Cross product of the particles velocity vector and the magnetic field vector)

3. The attempt at a solution
I've combined these equations to come up with a single equation for the magnitude of the force on the particle:

$F=\frac{q*v*μ_{0}*i*sin(θ)}{2\pi{r}}$

However this final equation is the part I am not confident on. I've proceeded on the basis the the magnetic field around an infinite wire carrying current is non-uniform; that is the direction of the magnetic field is not constant, but would appreciate my working being checked!

Last edited: Feb 21, 2013
2. Feb 20, 2013

### Staff: Mentor

Re: Calculate the force on a particle from magnetic field of infinite

The magnetic field is not constant, this will change sin(θ) and r in a trajectory. But the equation for the force at a specific radius with a specific angle is correct.
Current is written with a capital I. "i" is usually the imaginary unit.

3. Feb 20, 2013

### rude man

Re: Calculate the force on a particle from magnetic field of infinite

Looks good.

BTW i = √(-1) is only for physicists.

Real men (engineers) use j = √(-1) and i is very regularly used to denote current

4. Feb 20, 2013

### Staff: Mentor

Re: Calculate the force on a particle from magnetic field of infinite

And mathematics as well.

5. Feb 20, 2013

### rude man

Re: Calculate the force on a particle from magnetic field of infinite

Yeah, but not real men (and women)!

6. Feb 20, 2013

### eviljay

Thanks both! Just needed that extra pair of eyes to look at it