Solution: Click For PDF Version (a)
As the outer
and the inner surfaces of the coaxial cable are connected to a
battery of emf
where b is the outer radius and a is the inner radius of the cable. As the cable forms a circuit with a resistor of resistance R connected to the battery, there will be a current flow of magnitude
Because of the current flow in the inner part of the coaxial cable and the cylindrical symmetry of the cable there will be a circular magnetic field about the axis of the cable of magnitude
(b)
The magnetic
field vector
(c)
Integrating
the Poynting vector
As
the power flowing inside the cable
is equal to the Joule dissipation of the energy by the resistor. |
and a resistance R, as shown in the figure.
(a) We have to calculate E, B for
;
(b) calculate the Poynting vector
for
.
We have to answer whether this is reasonable.
(d) We have to show that the direction of
and the electric field vector
will be perpendicular to each other and it can be seen that
will be parallel to the axis of cable pointing in the direction of
the flow of current from the battery to the resistor. Therefore, the
magnitude of
over any annular cross section of the cable, we can obtain the power
flowing inside the cable. We find
,