An alternating electric field, of frequency v, is applied

An alternating electric field, of frequency v, is applied across the dees (radius = R) of a cyclotron that is being used to accelerate protons (mass = m). The operating magnetic field (B) used in the cyclotron and the kinetic energy (K) of the proton beam, produced by it, are given by :

Time period of cyclotron is

T =	1	=	2πm	; B =	2πm	Ʋ ; R =	mƲ	=	p
	Ʋ		eB		e		eB		eB

⇒ P = eBR = e ×	2πmƲ	R = 2πmƲ
	e

K.E. =	p²	=	(2πmƲR)²	= 2π²mƲ²R²
	2m		2m

B =	mv	and K = 2mπ²v²R²
	e

B =	2πmv	and K = m²πvR²
	e

B =	2πmv	and K = 2mπ²v²R²
	e

B =	mv	and K = m²πvR²
	e