# Lienard-Wiechert fields for low velocity source

I would like to use the Lienard-Wiechert E and B field expressions for a slowly moving charge where $\beta = v/c << 1$.

Is there an accepted approximate form to use?

Can one just set $\gamma = 1$ and the retardation factors $1 - \mathbf{n} . \mathbf{\beta}=1$ in the standard expressions for E and B?

There are many ways to do approximations. If you want to make mathematically reliable approximation instead of an "easy" one, I would use Taylor expansion in $\mathbf v/c$ around zero. Then you have to decide on the order of accuracy you want to use - if you want to have velocity dependence, you need to preserve constant and first order terms in $\mathbf v /c$. Then you can replace $\gamma$ by 1, because it does not have linear term in $\mathbf v/c$, but you cannot replace terms proportional to $1-\mathbf v/c\cdot\mathbf n$ by 1 - you need to keep them.