FrontierScience / 516da073-8d2a-4db5-a739-c752655ec14c / Consider a long straight conducting cylinder with a radius of `a`, the central axis of the cylinder as the `z`-axis, and located at `x=y=0`, placed in a uniform external electric f…

Consider a long straight conducting cylinder with a radius of `a`, the central axis of the cylinder as the `z`-axis, and located at `x=y=0`, placed in a uniform external electric field `(E)→₀=E₀(x)^`. Apply cylindrical coordinates (where \\(\\theta\\) is measured anticlockwise from the polar axis) to this system where the `x`-axis is aligned to the polar axis (\\(\\theta = 0\\)). Assume all physical quantities are independent of the `z` coordinate. If the potential at the conducting cylinder is `0`, find the electric field distribution `E(r,θ)` outside the conductor, in terms of \\(E_0, a, r, \\theta, \\hat{r}, \\hat{\\theta} \\).

Think step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.

Consider a long straight conducting cylinder with a radius of `\(a\)`, the central axis of the cylinder as the `\(z\)`-axis, and located at `\(x=y=0\)`, placed in a uniform external electric field `\(\overrightarrow{E}_0=E_0 \hat{x}\)`. Apply cylindrical coordinates (where \\(\\theta\\) is measured anticlockwise from the polar axis) to this system where the `\(x\)`-axis is aligned to the polar axis (\\(\\theta = 0\\)). Assume all physical quantities are independent of the `\(z\)` coordinate. If the potential at the conducting cylinder is `\(0\)`, find the electric field distribution `\(E(r,\theta)\)` outside the conductor, in terms of \\(E_0, a, r, \\theta, \\hat{r}, \\hat{\\theta} \\).

Think step by step and solve the problem below. At the end of your response, write your final answer on a new line starting with “FINAL ANSWER”. It should be an answer to the question such as providing a number, mathematical expression, formula, or entity name, without any extra commentary or providing multiple answer attempts.