Description
1. A thick wire of radius R carries a constant current I, which is uniformly distributed over
its cross section. A narrow gap in the wire of width w, where w ⌧ R, forms a parallel
-plate capacitor, as shown in Fig. 7.45.
Find the B~ -field in the gap, at a distance s<R from the axis.
2. Reconsider Problem 7 from Homework Set 12 of an alternating current I(t) = I0 sin(!t)
flowing down a long straight wire and returning along a coaxial conducting tube of radius
b. The electric field was found to take the form
E~ (s, t) = µ0I0!
2⇡
ln ✓b
s
◆
cos(!t)ˆz. (1)
a) Find the displacement current density J~
d.
b) Integrate the displacement current to get the total displacement current
Id =
Z
J~
d · d~a. (2)
c) Compare Id and I by calculating their ratio. If the outer cylinder had a radius of
b = 0.5 cm, how high would the frequency have to be for Id to be 1% of I?
