Question

derive formula of electric feild at any point due to a charged rod

Answer 1

$E_\perp = \frac{\lambda}{4\pi\epsilon_0 r} (\sin\theta_1 + \sin\theta_2), E_\parallel = \frac{\lambda}{4\pi\epsilon_0 r} (\cos\theta_1 - \cos\theta_2)$

Answer 2

The electric field at any point due to a charged rod can be derived by integrating the contribution of each infinitesimal charge element along the rod. The resulting formulas express the perpendicular and parallel components of the electric field with respect to the rod, dependent on the linear charge density, distance from the rod, and angles subtended by the ends of the rod at the point of interest.