There is a uniform electric field of strength | vedclass

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Question

(C) Given: Electric field $E = 10^3 \ V/m$ along the $Y$-axis,mass $m = 1 \ g = 10^{-3} \ kg$,charge $q = 10^{-6} \ C$,initial velocity $u_x = 10 \ ms

Vedclass · Accepted Answer

$10 \sqrt{2}$

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(C) Given: Electric field $E = 10^3 \ V/m$ along the $Y$-axis,mass $m = 1 \ g = 10^{-3} \ kg$,charge $q = 10^{-6} \ C$,initial velocity $u_x = 10 \ ms^{-1}$ along the $X$-axis,and time $t = 10 \ s$.Since the electric field is along the $Y$-axis,the force on the charge is $F_y = qE = 10^{-6} 	imes 10^3 = 10^{-3} \ N$.The acceleration along the $Y$-axis is $a_y = F_y / m = 10^{-3} / 10^{-3} = 1 \ ms^{-2}$.The velocity along the $X$-axis remains constant as there is no force in that direction: $v_x = u_x = 10 \ ms^{-1}$.The velocity along the $Y$-axis after $10 \ s$ is $v_y = u_y + a_y t = 0 + (1 	imes 10) = 10 \ ms^{-1}$.The resultant speed $v = \sqrt{v_x^2 + v_y^2} = \sqrt{10^2 + 10^2} = \sqrt{200} = 10 \sqrt{2} \ ms^{-1}$.

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