Charge passing through a conductor of cross-s | vedclass

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(B) Given: Area $A = 0.3 ~m^2$,charge density $n = 2 	imes 10^{25} / m^3$,and charge $q = 3t^2 + 5t + 2$.First,find the current $i$ by differentiatin

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$1.77 	imes 10^{-5} ~m/s$

Vedclass · Answer

(B) Given: Area $A = 0.3 ~m^2$,charge density $n = 2 	imes 10^{25} / m^3$,and charge $q = 3t^2 + 5t + 2$.First,find the current $i$ by differentiating $q$ with respect to time $t$:$i = \frac{dq}{dt} = \frac{d}{dt}(3t^2 + 5t + 2) = 6t + 5$.At $t = 2 ~s$,the current is $i = 6(2) + 5 = 17 ~A$.The relationship between current and drift velocity $v_d$ is given by $i = neAv_d$.Rearranging for $v_d$:$v_d = \frac{i}{neA}$.Substituting the values $(e = 1.6 	imes 10^{-19} ~C)$:$v_d = \frac{17}{2 	imes 10^{25} 	imes 1.6 	imes 10^{-19} 	imes 0.3}$.$v_d = \frac{17}{0.96 	imes 10^6} = 17.708 	imes 10^{-6} ~m/s = 1.77 	imes 10^{-5} ~m/s$.

Charge passing through a conductor of cross-section area $A=0.3 ~m^2$ is given by $q=3 t^2+5 t+2$ in coulomb,where $t$ is in second. What is the value of drift velocity at $t=2 ~s$ ? (Given,$n=2 \times 10^{25} / m^3$ )

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