equal to B1 on one side of the plane and to 132, on the other. Find
the magnetic force acting per unit area of the plane in the cases
illustrated in Fig. 3.72. Determine the direction of the current in
the plane in each case.
3.261. In an electromagnetic pump designed for transferring molten metals a pipe section with metal is located in a uniform magnetic
field of induction B (Fig. 3.73). A current
I is made to flow across this pipe section
11
in the direction perpendicular both to the
vector B and to the axis of the pipe. Find
the gauge pressure produced by the pump
if B = 0.10 T, I= 100 A, and a= 2.0 cm.
3.262. A current I flows in a long thinwalled cylinder of radius R. What pressure
do the walls of the cylinder experience?
3.263. What pressure does the lateral
surface of a long straight solenoid with n
turns per unit length experience when a current I flows through it?
3.264. A current I flows in a long single-layer solenoid with crosssectional radius R. The number of turns per unit length of the solenoid equals n. Find the limiting current at which the winding may
rupture if the tensile strength of the wire is equal to Fiim.
3.265. A parallel-plate capacitor with area of each plate equal to
S and the separation between them to d is put into a stream of conducting liquid with resistivity p. The liquid moves parallel to the
plates with a constant velocity v. The whole system is located in
a uniform magnetic field of induction B, vector B being parallel to
the plates and perpendicular to the stream direction. The capacitor
plates are interconnected by means of an external resistance R.
What amount of power is generated in that resistance? At what
value of R is the generated power the highest? What is this highest
power equal to?
3.266. A straight round copper conductor of radius R = 5.0 mm
carries a current I = 50 A. Find the potential difference between
the axis of the conductor and its surface. The concentration of the
conduction electrons in copper is equal to n = 0.9.1023 cm-3.
3.267. In Hall effect measurements in a sodium conductor the
strength of a transverse field was found to be equal to E = 5.0 µV/cm
with a current density j = 200 A/cm2 and magnetic induction B =
= 1.00 T. Find the concentration of the conduction electrons and
its ratio to the total number of atoms in the given conductor.
3.268. Find the mobility of the conduction electrons in a copper
conductor if in Hall effect measurements performed in the magnetic
field of induction B = 100 mT the transverse electric field strength
of the given conductor turned out to be 3.1.103 times less than
that of the longitudinal electric field.
3.269. A small current-carrying loop is located at a distance r
from a long straight conductor with current I. The magnetic moment
Fig. 3.73.
143
the magnetic force acting per unit area of the plane in the cases
illustrated in Fig. 3.72. Determine the direction of the current in
the plane in each case.
3.261. In an electromagnetic pump designed for transferring molten metals a pipe section with metal is located in a uniform magnetic
field of induction B (Fig. 3.73). A current
I is made to flow across this pipe section
11
in the direction perpendicular both to the
vector B and to the axis of the pipe. Find
the gauge pressure produced by the pump
if B = 0.10 T, I= 100 A, and a= 2.0 cm.
3.262. A current I flows in a long thinwalled cylinder of radius R. What pressure
do the walls of the cylinder experience?
3.263. What pressure does the lateral
surface of a long straight solenoid with n
turns per unit length experience when a current I flows through it?
3.264. A current I flows in a long single-layer solenoid with crosssectional radius R. The number of turns per unit length of the solenoid equals n. Find the limiting current at which the winding may
rupture if the tensile strength of the wire is equal to Fiim.
3.265. A parallel-plate capacitor with area of each plate equal to
S and the separation between them to d is put into a stream of conducting liquid with resistivity p. The liquid moves parallel to the
plates with a constant velocity v. The whole system is located in
a uniform magnetic field of induction B, vector B being parallel to
the plates and perpendicular to the stream direction. The capacitor
plates are interconnected by means of an external resistance R.
What amount of power is generated in that resistance? At what
value of R is the generated power the highest? What is this highest
power equal to?
3.266. A straight round copper conductor of radius R = 5.0 mm
carries a current I = 50 A. Find the potential difference between
the axis of the conductor and its surface. The concentration of the
conduction electrons in copper is equal to n = 0.9.1023 cm-3.
3.267. In Hall effect measurements in a sodium conductor the
strength of a transverse field was found to be equal to E = 5.0 µV/cm
with a current density j = 200 A/cm2 and magnetic induction B =
= 1.00 T. Find the concentration of the conduction electrons and
its ratio to the total number of atoms in the given conductor.
3.268. Find the mobility of the conduction electrons in a copper
conductor if in Hall effect measurements performed in the magnetic
field of induction B = 100 mT the transverse electric field strength
of the given conductor turned out to be 3.1.103 times less than
that of the longitudinal electric field.
3.269. A small current-carrying loop is located at a distance r
from a long straight conductor with current I. The magnetic moment
Fig. 3.73.
143