Question

13. ssm Three charges are fixed t charge of +18 pC is on the y axis at y +3.0 m. A charge of -12 μC is at the origin. Lastly, a charge of +45 pC is on the x o an xy coorainate sysicuı. ax is at +3.0 m. Determine the magnitude and direction of the net electrostatic force on the charge at x +3.0 m. Specify the direction relative to the -x axis. 22.

Answer 1

$F_{1}=kq_{1}q_{3}/r^{2}$

$r^{2}=3^{2}+3^{2}=18$

$F_{1}=9*10^{9}*1.8*10^{-5}*4.5*10^{-5}/18$

$F_{1}=0.405N$

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$F_{2}=kq_{2}q_{3}/r^{2}$

$F_{2}=9*10^{9}*1.2*10^{-5}*4.5*10^{-5}/3^{2}$

$F_{2}=0.54N$

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Triangle 123 is a right angled isosceles triangle ,so inside angles are 45 deg ,45 deg and 90 deg

$F_{x}=F_{1}sin45 -F_{2}$

$F_{x}=0.405Nsin45 -0.54N$

${\color{Red} F_{x}=-0.254N}$

$F_{y}=-F_{1}cos45$

$F_{y}=-0.405Ncos45$

${\color{Red} F_{y}=-0.286N}$

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$F=\sqrt{F_{x}^{2}+F_{y}^{2}}$

$F=\sqrt{(0.254)^{2}+(0.286)^{2}}$

ANSWER: ${\color{Red} F=0.3825N}$

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Direction

$tan\theta =F_{y}/F_{x}$

$\theta =tan^{-1}(F_{y}/F_{x})$

$\theta =tan^{-1}(-0.286/-0.254)$

ANSWER: ${\color{Red} \theta =48.39^{\circ}}$ with respect to -ve x axis (3rd Quadrant )

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