tan a 2 /tan al = a,/cri, where al and a2 are the conductivities of
the media, a 2 and al are the angles between the current lines and the
normal of the boundary surface.
3.165. Two cylindrical conductors with equal cross-sections and
different resistivities pi and (3 2 are put end to end. Find the charge
at the boundary of the conductors if a current I flows from conductor
1 to conductor 2.
3.166. The gap between the plates of a parallel-plate capacitor is
filled up with two dielectric layers 1 and 2 with thicknesses d 1 and
d 2 , permittivities 8, and 8 2 , and resistivities Pi and p 2. A de voltage
V is applied to the capacitor, with electric field directed from layer 1
to layer 2. Find a, the surface density of extraneous charges at the
boundary between the dielectric layers, and the condition under
which a = 0.
3.167. An inhomogeneous poorly conducting medium fills up
the space between plates 1 and (^2) of a parallel-plate capacitor. Its
permittivity and resistivity vary from values 8 1 , pi at plate 1 to
values 8 2 , P (^2) at plate 2. A de voltage is applied to the capacitor
through which a steady current I flows from plate (^1) to plate 2. Find
the total extraneous charge in the given medium.
3.168. The space between the plates of a parallel-plate capacitor
is filled up with inhomogeneous poorly conducting medium whose
resistivity varies linearly in the direction perpendicular to the plates.
The ratio of the maximum value of resistivity to the minimum
one is equal to 11 The gap width equals d. Find the volume density
of the charge in the gap if a voltage V is applied to the capacitor.
E is assumed to be 1everywhere.
3.169. A long round conductor of cross-sectional area S is made
of material whose resistivity depends only on a distance r from the
axis of the conductor as p = air', where a is a constant. Find:
(a) the resistance per unit length of such a conductor;
(b) the electric field strength in the conductor due to which a cur-
rent I flows through it.
3.170. A capacitor with capacitance C = 400 pF is connected
via a resistance R = 650 Q to a source of constant voltage Vo.
How soon will the voltage developed across the capacitor reach a
value V = 0.90 Vo?
3.171. A capacitor filled with dielectric of permittivity e = 2.1
loses half the charge acquired during a time interval i = 3.0 min.
Assuming the charge to leak only through the dielectric filler, cal-
culate its resistivity.
3.172. A circuit consists of a source of a constant emf e and a resist
ante R and a capacitor with capacitance C connected in series. The
internal resistance of the source is negligible. At a moment t =^0
the capacitance of the capacitor is abruptly decreased 1-fold. Find
the current flowing through the circuit as a function of time t.
3.173. An ammeter and a voltmeter are connected in series to a bat-
tery with an emf F = 6.0 V. When a certain resistance is connected