A line charge of uniform charge density \(\rho_{0} \mathrm{C} / \mathrm{m}\) and of length \(\ell\) is oriented along the \(z\) axis at \(-\ell / 2

Question: Given a line charge of uniform charge density ρ_0 C/m and length ℓ oriented along the z-axis from -ℓ/2 to ℓ/2, find the electric field strength at any position along the x-axis. In part (b), determine the force acting on an identical line charge oriented along the x-axis at ℓ/2 < x < 3ℓ/2. Answer: To find the electric field strength at any position along the x-axis, we need to integrate the electric field contribution from each small charge segment within the line charge. This is done by finding the x-component of the electric field and integrating it over the full length of the line charge from -ℓ/2 to ℓ/2. After performing the integration, we will find the electric field strength at any position along the x-axis, E_x. For part (b), to find the force acting on an identical line charge oriented along the x-axis between ℓ/2 and 3ℓ/2, we need to multiply the electric field found in part (a) with the charge density ρ_0 and integrate it over the given length. After performing the integration, we will find the force acting on the line charge.