# Magnetic Field Does Zero Work

1. May 15, 2013

### conorordan

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

This isn't strictly homework, I'm going over my lecturer's notes before the exam and I don't understand a part of this proof for magnetic fields doing no work.

This is the second proof he gave, the first being the more standard $\vec{B}\cdot\textit{d}\vec{l}=0$

2. Relevant equations

So in the second proof he does it like this;

I cannot figure out where he gets the factor of a half in the third line, to make the equation come out as change in kinetic energy = 0.

2. May 15, 2013

### tiny-tim

hi conorordan!
product rule

d(v·v)/dt = v·dv/dt + dv/dt·v = 2 v·dv/dt