THESE QUESTIONS ARE RELATED PHY250: (ELECTRO MAGNETICS):

9) (3) Use Gauss's law to find the electric field inside and outside a long straight wire of radius R with uniform charge density p (b) Integrate E to find the potential inside and outside the wire with the boundary condition (R) 0 10) In an atom you might expect the electric potential from the nucleus to behave like l/r , where r is the distance from the nucleus. The nucleus is we and it has -ve electrons around it. Those electrons screen the nuclear charge, and lead to a potential that drops off exponentially. (3) Find the electric field produced by a potential I 9"\" "Wmlq r l 0 The charge q is at the origin. Remember that E is a vector, and in your expression for the field keep terms in l/r and l/r2 separate this just makes the next step easier. Remember that l/r has a pole at the origin, so write the charge distribution as the sum of the part at r=0 and the rest of space. Think about the value of V-( f/rz) The charge distribution has two terms (due to the pole) can you interpret what they correspond to physically? (b) Find the charge distribution that produces this potential (c) Show that your answers satisfy Gauss's Law. Use a spherical Gaussian surface, and be careful about the origin. You'll need to use integration by parts in the final step