Two charges +10 mu C and -10 mu C are separat | vedclass

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Question

$(A)$ Let the charges be $q_1 = +10 \mu C$, $q_2 = -10 \mu C$, and the test charge be $q_0 = 5 \mu C$. The distance between $q_1$ and $q_2$ is $d = 10

Vedclass · Accepted Answer

$360$

Vedclass · Answer

$(A)$ Let the charges be $q_1 = +10 \mu C$, $q_2 = -10 \mu C$, and the test charge be $q_0 = 5 \mu C$. The distance between $q_1$ and $q_2$ is $d = 10 	ext{ cm} = 0.1 	ext{ m}$.The test charge $q_0$ is placed at the midpoint, so the distance from each charge is $r = 5 	ext{ cm} = 0.05 	ext{ m}$.The force exerted by $q_1$ on $q_0$ is $F_1 = \frac{1}{4 \pi \varepsilon_0} \frac{q_1 q_0}{r^2}$ (repulsive, directed towards $q_2$).The force exerted by $q_2$ on $q_0$ is $F_2 = \frac{1}{4 \pi \varepsilon_0} \frac{|q_2| q_0}{r^2}$ (attractive, directed towards $q_2$).Since both forces are in the same direction, the total force is $F = F_1 + F_2 = 2 	imes \frac{9 	imes 10^9 	imes 10 	imes 10^{-6} 	imes 5 	imes 10^{-6}}{(0.05)^2}$.$F = 2 	imes \frac{9 	imes 10^9 	imes 50 	imes 10^{-12}}{25 	imes 10^{-4}} = 2 	imes \frac{450 	imes 10^{-3}}{25 	imes 10^{-4}} = 2 	imes 18 	imes 10 = 360 	ext{ N}$.

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