`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 induc-

tion 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 trajecto-

ry between two nearest points at which the

velocity of the particle turns into zero;

(c) the mean value of the particle's veloc-

ity 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 pro-

ducing a magnetic field in the surrounding space. Find the least po-

tential difference between the cathode and anode at which the thermal

electrons leaving the cathode without initial velocity start reach-

ing 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 po-

tential 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 perpendicu-

lar electric and magnetic fields. The magnetic field is constant and

`Fig. 3.104.`

11*