A 1 mu A beam of protons with a cross-section | vedclass

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(B) The current $i$ is given as $1 \mu A = 10^{-6} 	ext{ A}$.The cross-sectional area $A = 0.5 	ext{ mm}^2 = 0.5 	imes 10^{-6} 	ext{ m}^2$.The vel

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$6.6 	imes 10^{-5} 	ext{ C/m}^3$

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(B) The current $i$ is given as $1 \mu A = 10^{-6} 	ext{ A}$.The cross-sectional area $A = 0.5 	ext{ mm}^2 = 0.5 	imes 10^{-6} 	ext{ m}^2$.The velocity of the protons $v = 3 	imes 10^4 	ext{ m/s}$.In one second,the length of the beam segment is $L = v 	imes t = 3 	imes 10^4 	imes 1 = 3 	imes 10^4 	ext{ m}$.The volume of this segment is $V = A 	imes L = (0.5 	imes 10^{-6} 	ext{ m}^2) 	imes (3 	imes 10^4 	ext{ m}) = 1.5 	imes 10^{-2} 	ext{ m}^3$.The charge flowing in one second is $Q = i 	imes t = 10^{-6} 	ext{ C} 	imes 1 	ext{ s} = 10^{-6} 	ext{ C}$.Charge density $ho = \frac{Q}{V} = \frac{10^{-6}}{1.5 	imes 10^{-2}} = \frac{1}{1.5} 	imes 10^{-4} = 0.666 	imes 10^{-4} = 6.66 	imes 10^{-5} 	ext{ C/m}^3$.Thus,the correct option is $B$.

$A$ $1 \mu A$ beam of protons with a cross-sectional area of $0.5 \text{ mm}^2$ is moving with a velocity of $3 \times 10^4 \text{ m/s}$. The charge density of the beam is:

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