Shown is a coaxial cable, made of an inner
cylindrical conducting wire of radius a and
an outer conducting sheath of inner radius
b. The wire carries uniform positive charge per unit length ? . The
sheath is grounded (V = 0). Also shown is a cross section, with a point (indicated by the dot) at distance r from the symmetry axis.
a. What is the charge per unit length on the inner surface of
sheath? What is the direction of E at the indicated point? How do you know?
b. Use Gauss’s law (using a cylindrical surface passing through the point) to find the magnitude of the E-field at the point indicated. Ans: E = 2k? / r .
c. Find the potential on the wire’s surface. Ans: V(a) = 2k? ? ln(b/ a) .