Question 185: Electromagnetic Induction

Question

If the maximum value of accelerating potential provided by a ratio frequency oscillator is 12 kV. The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is ...............[mp = 1.67 $$	imes$$ 10$$-$$27 kg, e = 1.6 $$	imes$$ 10$$-$$19C, Speed of light = 3 $$	imes$$ 108 m/s]

Accepted Answer

V = 12 kV
Number of revolution = n
$$n[2 	imes {q_P} 	imes V] = {1 \over 2}{m_P} 	imes v_P^2$$
$$n[2 	imes 1.6 	imes {10^{ - 19}} 	imes 12 	imes {10^3}]$$
$$ = {1 \over 2} 	imes 1.67 	imes {10^{ - 27}} 	imes {\left[ {{{3 	imes {{10}^8}} \over 6}} ight]^2}$$
n(38.4 $$	imes$$ 10
$$-$$16
) = 0.2087 $$	imes$$ 10
$$-$$11
n = 543.4

Electromagnetic Induction

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