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Electrodynamics (I): Homework 2 Due: October 16, 2014 Exercises in Griffiths 1.46, 2.6, 2.9, 2.10 (5%, hand-in), 2.15, 2.16, 2.18(5% hand-in), 2.20, 2.21, 2.22, 2.26, 2.33 (5%, hand-in), 2.36, 2.37, 2.39 (5% hand-in), 2.54(35 %, hand-in) Ex.1 hand-in 10% The electric field for a static charge distribution is given by −αr ~ = ke E r2 r̂, (1) where k and α are positive constants and r̂ is a unit vector along radial direction. Find the charge density at r and the total charge of this charge distribution. Ex.2 hand-in Suppose that the electric field due to a point charge q deviates from the form r̂ r2 and were given by ~ = E q r̂ , 4π0 r2+ (2) where the deviation is very small and satisfies 1. ~ and ∇ × E ~ for r 6= 0. Show that one can still define the electric (a) 5 % Calculate ∇ · E potential and find the electric potential φ for a point charge q by setting the potential zero at r = ∞. (b) 10% Consider a spherical shell of radius a that carries charge Q. If the charge is uniformaly distributed in the spherical shell, find the electric potential φ(r) at a distance r < a from the center of the sphere and reveal the difference due to . 1