Question

6. You are in a region of space where the electric potential is given by: V(x, y,z) Voxy In(z) ( for all points where z>0 (above the x-y plane) ) Find an expression for the electric field E(x, y,z). State this vectorially. 7. In physical wires that carry current, the majority of the current will actually travel very close to the the outer edge of the wire (in the same way that static charge deposited on a conductor will spread across its surface rather than its interior). One way to model the physical flow of charge through a cylindrical wire of radius R is with the following current density function: J(r) = Jor4k with Jo = 2.5 x 106A/㎡SI 30° Note that this is only true for r s R (inside the conducting wire) and that it points in the +z direction 1everywhere (hence the k). Assume that no charges are present outside the conducting wire. a) Calculate the total current carried through a wire of radius R 1.0 cm. b) Use Ampere's Law to find an expression for the magnetic field B(r) everywhere inside the wire. Sketch the magnitude of B(r) as a function of radius. Evaluate the magnetic field strength at the surface of the wire. c) 8. In the setup shown to the right, a long straight wire caries a time-varying (ie, nt unwards Directly next to it, in the same plane, lies a rectangular

Please Help with all of Number 7.

Answer 1