# Electrodynamics and vector calculus question

1. Oct 23, 2012

### goodnews

1. The problem statement, all variables and given/known data

1) The magnetic field everywhere is tangential to the magnetic field lines, $\vec{B}$=B[$\hat{e}t$], where [$\hat{e}$][/t] is the tangential unit vector. We know $\frac{d\hat{e}t}{ds}$=(1/ρ)[$\hat{e}$][/n]
, where ρ is the radius of curvature, s is the distance measured along a field line and [$\hat{e}$][/n] is the normal unit vector to the field line.

Show the radius of curvature at any point on a magnetic field line is given by ρ=$\frac{B^3}{abs(\vec{B}X(\vec{B}\bullet\vec{B})\vec{B}) }$

2. Relevant equations
$\vec{B}$=B[$\hat{e}$][/t]
$\frac{d\hat{e}t}{ds}$=(1/ρ)[$\hat{e}$][/n]
ρ=$\frac{B^3}{abs(\vec{B}X(\vec{B}\bullet\vec{B})\vec{B}) }$

3. The attempt at a solution
solved the vector equation, and would then use some form of stokes theorem to equate it and find the value of ρ

Last edited: Oct 23, 2012