How well do you know electricity and magnetism ?

The magnetic field $B$ at a point radial distance $r$ from an infinite wire carrying current $I$ is given by:

$B = \frac{\mu_0I}{2 \pi r}$

From electromagnetic wave equation: $\left(c^2\nabla^2 - \frac{\partial^2}{\partial t^2} \right) \text{E} = 0 \\ \left(c^2\nabla^2 - \frac{\partial^2}{\partial t^2} \right) \text{B} = 0$

where $c = \dfrac{1}{\sqrt{\mu_0 \epsilon_0}}$ , $c$ is the speed of light, and $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space.

In a universe, where $c \to \infty$ , since the wave equation is symetrical $\mu_0 \to 0$ and $\epsilon_0 \to 0$ , and $B = \boxed{0}$ .

μ°approaches 0 by -Can we say by expression c=1/√μ°*€°

Thus the magnetic field exist because the speed of light is finite in our universe $B=0$ .

Mathematical proof:

By Lorent'z transformations we know

$\vec B_n'=\gamma(\vec B_n-(\vec v \times \vec E)/c^2)$

Now let K be the system moving with current and K' be the system of observation. Then in K $B_n=0$ and because $c$ is infinity $(\vec v \times \vec E)/c^2=0$ so $B_n'=0$ .