Response:
Reasoning:
We will utilize a Gaussian surface that resembles the curved wall of a cylinder, with a radius of 3mm and a length of 1 unit directed parallel to the wire axis.
The charge within this cylinder amounts to 250 x 10⁻⁹ C.
Let E denote the electric field at the curved surface, perpendicular to it.
The total electric flux leaving the curved surface
is calculated as 2π r x 1 x E
or 2 x 3.14 x 3 x 10⁻³ E
According to Gauss's law, the total flux is given by the charge within divided by ε (the charge inside the cylinder being 250 x 10⁻⁹C)
equals 250 x 10⁻⁹ / 2.5 x 8.85 x 10⁻¹² (where ε = 2.5 ε₀ = 2.5 x 8.85 x 10⁻¹²)
resulting in 11.3 x 10³ weber.
Thus,
2 x 3.14 x 3 x 10⁻³ E = 11.3 x 10³
E = 11.3 x 10³ / 2 x 3.14 x 3 x 10⁻³
=.599 x 10⁶ N /C.