$9.2.3.$ Find the distribution of magnetic field induction around an infinite straight wire carrying a current $I$.
We write down the current strength by definition, we find the speed of current flow $$ I = \frac{dq}{dt} = \frac{\lambda dl}{dt} = \lambda v \Rightarrow v = \frac{I}{\lambda} $$ Field of a charged filament with linear charge density $\lambda$: $$ E = \frac{\lambda}{2\pi\varepsilon_0 R} $$ Where do we find the distribution of magnetic field induction around the wire? $$ B = \varepsilon_0 \mu_0 Ev\Rightarrow \boxed{B = \frac{\mu_0 I}{2\pi R}} $$
$$B = \frac{\mu_0 I}{2\pi R}$$