$\newcommand{\tl}[1]{\tag{#1}\label{#1}}$
Magnetic Field of a current is: $$B = \mu_0 I / (2 \pi r)\tl{01}$$ Magnetic Field of a Moving Charge is: $$B = \mu_0 qv\sin\theta / (4\pi r^2)\tl{02}$$
So I have $$\mu_0 I / (2\pi r) = \mu_0 qv\sin\theta / (4\pi r^2)\implies I = qv\sin\theta / (2r)\tl{03}$$ Since $I = q/t$, $$q/t = qv\sin\theta / (2r)\implies vt\sin\theta = 2r\tl{04}$$ Since $l = vt$, $$l\sin\theta = 2r\implies\frac{l}{r}\sin\theta = 2\tl{05}$$ Since $l / r =\cos\theta$, $$\cos\theta\sin\theta = 2\tl{06}$$
This equation has no solution. It doesn't make sense. Can someone please point out where I'm wrong at?
What I write is just what I think in my head, if you don't understand something, please ask me because you may not find it on any website.
