3.391. A beam of non-relativistic charged particles moves without
deviation through the region of space A (Fig. 3.103) where there are
transverse mutually perpendicular electric and magnetic fields with
S
Fig. 3.103.
strength E and induction B. When the magnetic field is switched off,
the trace of the beam on the screen S shifts by 6.x. Knowing the
distances a and b, find the specific charge qlm of the particles.
3.392. A particle with specific charge qim moves in the region of
space where there are uniform mutually perpendicular electric and
magnetic fields with strength E and induction B (Fig. 3.104). At the moment t = 0
the particle was located at the point 0 and
had zero velocity. For the non-relativistic
case find:
(a) the law of motion x (t) and y (t) of the
particle; the shape of the trajectory;
(b) the length of the segment of the trajectory between two nearest points at which the
velocity of the particle turns into zero;
(c) the mean value of the particle's velocity vector projection on the x axis (the drift velocity).
3.393. A system consists of a long cylindrical anode of radius a
and a coaxial cylindrical cathode of radius b (b < a). A filament
located along the axis of the system carries a heating current I producing a magnetic field in the surrounding space. Find the least potential difference between the cathode and anode at which the thermal
electrons leaving the cathode without initial velocity start reaching the anode.
3.394. Magnetron is a device consisting of a filament of radius a
and a coaxial cylindrical anode of radius b which are located in a
uniform magnetic field parallel to the filament. An accelerating potential difference V is applied between the filament and the anode.
Find the value of magnetic induction at which the electrons leaving
the filament with zero velocity reach the anode.
3.395. A charged particle with specific charge qim starts moving
in the region of space where there are uniform mutually perpendicular electric and magnetic fields. The magnetic field is constant and
Fig. 3.104.
11*
deviation through the region of space A (Fig. 3.103) where there are
transverse mutually perpendicular electric and magnetic fields with
S
Fig. 3.103.
strength E and induction B. When the magnetic field is switched off,
the trace of the beam on the screen S shifts by 6.x. Knowing the
distances a and b, find the specific charge qlm of the particles.
3.392. A particle with specific charge qim moves in the region of
space where there are uniform mutually perpendicular electric and
magnetic fields with strength E and induction B (Fig. 3.104). At the moment t = 0
the particle was located at the point 0 and
had zero velocity. For the non-relativistic
case find:
(a) the law of motion x (t) and y (t) of the
particle; the shape of the trajectory;
(b) the length of the segment of the trajectory between two nearest points at which the
velocity of the particle turns into zero;
(c) the mean value of the particle's velocity vector projection on the x axis (the drift velocity).
3.393. A system consists of a long cylindrical anode of radius a
and a coaxial cylindrical cathode of radius b (b < a). A filament
located along the axis of the system carries a heating current I producing a magnetic field in the surrounding space. Find the least potential difference between the cathode and anode at which the thermal
electrons leaving the cathode without initial velocity start reaching the anode.
3.394. Magnetron is a device consisting of a filament of radius a
and a coaxial cylindrical anode of radius b which are located in a
uniform magnetic field parallel to the filament. An accelerating potential difference V is applied between the filament and the anode.
Find the value of magnetic induction at which the electrons leaving
the filament with zero velocity reach the anode.
3.395. A charged particle with specific charge qim starts moving
in the region of space where there are uniform mutually perpendicular electric and magnetic fields. The magnetic field is constant and
Fig. 3.104.
11*