1. The problem statement, all variables and given/known data Is it possible to create an electrostatic field E(x) (in 3 spatial dimensions x and E is a vector of course) such that i) E(x) = a × x (cross product) ii) E(x) = (a.x) b (dot product between a and x) where a,b and non-zero vectors that do not depend on time and the spatial coordinates. I also have to stay the condition on the constant vectors a and b. 2. A ball of radius R charged homogeneously throughout its volume is centered at the origin. i) Find the charge density rho(x) for each point of space time ii) Find the electric field E(x) created by the charged ball. Not sure how to approach this question, I'm comfortable with working with point charges and using the delta distribution but not for a charged ball. 2. Relevant equations I suspected Maxwell's equations would come in handy for the first question but I have been unable to use them to get any conclusion. Many thanks.