Consider having a long, thin nanowire placed along the 𝑥-axis. This nanowire has a uniform linear charge density 𝜆. Surrounding the nanowire, you have a cubic box made of a special transparent dielectric material, which allows you to observe the electric field lines without distortion. The cube has an edge length 𝐿 and is centered on the nanowire, such that the nanowire passes through the center of the cube. Consider the face parallel to the xz-plane. Define the small area 𝑑𝐴 as a strip of width 𝑑𝑧 and length 𝐿 with the vector pointing in the -y-direction. Utilize the established electric field of a wire to determine the electric flux 𝑑Φ through this small area. Express your formula in terms of the variable 𝑧 and relevant constants, ensuring it does not explicitly include any angles.
Consider having a long, thin nanowire placed along the 𝑥-axis. This nanowire has a uniform linear charge density 𝜆. Surrounding the nanowire, you have a cubic box made of a special transparent dielectric material, which allows you to observe the electric field lines without distortion. The cube has an edge length 𝐿 and is centered on the nanowire, such that the nanowire passes through the center of the cube. Consider the face parallel to the xz-plane. Define the small area 𝑑𝐴 as a strip of width 𝑑𝑧 and length 𝐿 with the vector pointing in the -y-direction. Utilize the established electric field of a wire to determine the electric flux 𝑑Φ through this small area. Express your formula in terms of the variable 𝑧 and relevant constants, ensuring it does not explicitly include any angles.