1. The problem statement, all variables and given/known data A line of charge of uniform density ρl occupies a semicircle of radius b as shown in Fig. P4.10. Use the material presented in Example 4-4 to determine the electric field at the origin. 2. Relevant equations dE = kdQ/r^2 3. The attempt at a solution I'm trying to understand the solution given in the solutions manual, here it is: http://www.zmuda.ece.ufl.edu/Fields_1_Spring 2013/4-1.10.pdf 1. Why is the direction -r hat, rather than just r hat? 2. Why is the enclosed charge Q stated as (pl)(b)? Shouldn't it be pl multiplied by the arc length of the half circle? I understand that I'm wrong and the solution is right, but I do not understand why the charge density would be multiplied by the radius.