(a) The figure below shows a thin plastic rod of length L and uniform positive charge density of ̴̴́̀̀. Find an expression of the electric potential at point P in terms of ̴̴́̀̀, a, b and L, by integration formula. (Hint: ∫ dx/√(x²+a²) = ln(x + √(x²+a²)) + C)
(c) A face consists of 6 items as shown in the following figure.
A thin rod of charge +20 nC/m forms a circle of radius 1.5r.
A thin circular arc of charge + 10 nC and radius r.
Two point charges of charge -2 nC each.
Two linear thin rod of charge -4 nC each.
Given a = 0.5 cm, b = 2.5 cm, c = 2 cm, d = 1 cm, L = 2 cm, and r = 3.2 cm.
Using the result in part (a), determine the net electric potential at the center, P.