The charge density and current of an infinitely long perfectly conducting wire of radius a, which lies along the z-axis, as measured by a static observer are zero and a constant I, respectively. The charge density measured by an observer, who moves at a speed v = βc parallel to the wire along the direction of the current, is
1
\(-\frac{I \beta}{\pi a^2 c \sqrt{1-\beta^2}}\)
2
\(-\frac{I \beta \sqrt{1-\beta^2}}{\pi a^2 c}\)
3
\(\frac{I \beta}{\pi a^2 c \sqrt{1-\beta^2}}\)
4
\(\frac{I \beta \sqrt{1-\beta^2}}{\pi a^2 c}\)