3.380. (a) p=qrB; T =m^0 c^2 (1/ 1+ (qrBlm- oc)^2 —1); (c) w =
C^2(1) (^) mv
leB
3.384. r 2p I sin (cp/2) I , where p —m eB (^) y sin a, cos a
3.385. rmax---- aevo/b, where b= )1°— 2n m I.
3.386. v — V^ qlm V^
rB (b I a) '^ = r^2 B^2 In (b la)
3.387. (a) yn= 913 , ; (b) tan a = 2nEn •
2n 2 m En 2 vo B
3.388. z = 1 tan V -^2 —T;-^7 qB^1 y; for z <1 this equation reduces to
y = (2mElq1 2 B 2 ) z 2.
3.389. F = mEl I qB = 20 [IN.
3.390. Al —
2 nmE^ tan cp 6 cm.
eB 2
a (a+2b) B2
3.391. 2EAx •
3.392. (a) x = a (cot — sin cot); y = a (1 — cos cot), where a =
= mElqB 2 , co qB/m. The trajectory is a cycloid (Fig. 26). The
y
2u
,z•
Fig. 26.
motion of the particle is the motion of a point located at the rim
of a circle of radius a rolling without slipping along the x axis so
that its centre travels with the velocity v = E/B; (b) s = 8mE/gB^2 ;
(c) (v x) = EIB.
3.393. V = 2 nt^21 4n -'^1 -) ln -^2 ab -
3.394. B< b'
2b VILa2 11 V.
3.395. y = t sin cot, x= ÷^2 (^0 (sin cot— cot cos cot), ,^ where
a = qEmlm. The trajectory has the form of unwinding spiral.
3.396. V > 2n 2 v 2 mrAr/e = 0.10 MV.
r [1+ (moclqrB)^2 ]•
3.381. T = imoc 2 , 5 keV and 9 MeV respectively.
3.382. Al = lac 2mv I eB 2 cos a= 2.0 cm.
8n2v
3.383. t^2 (B^2 —B^1 )^2 •