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
the

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* = 2*k*? / *r*
.

c. Find the potential on the wire’s surface. Ans:
*V*(*a*) = 2*k*? ? ln(*b*/ *a*)
.

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