Question

Find the electric potential V at a location a distance b from the origin in the x-y plane due to a line charge with charge density Pe and of length l, The line charge is coincident with the z-axis and extends from z = -1/2 to z = 1/2.

Answer 1

The student must integrate the electric potential contributions of a line charge with linear charge density ρe to find the electric potential at a distance b from the origin in the x-y plane.

Step-by-step explanation:

The student is seeking to calculate the electric potential V at a distance b from the origin due to a line charge with linear charge density ρe placed along the z-axis, extending from z = -1/2 to z = 1/2. The process involves integrating the contributions of electric potential from each infinitesimally small segment (dq) of the line charge, which can be considered a point charge. The infinitesimal electric potential dV caused by a charge dq at a distance r from a point in space is given by dV = k • dq/r, where k is Coulomb's constant. To find the total potential, integrate this expression along the length of the line charge, from -l/2 to l/2. The integration will likely involve the expression dq = ρe • dz and the geometric relationship r = √(b² + z²), where b is the perpendicular distance to the line charge in the x-y plane and z is the variable of integration.