Three charges 4q,Q,and q are placed in a stra | vedclass

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(A) Let the positions of the charges be $x_1 = 0$,$x_2 = l/2$,and $x_3 = l$.The force on charge $q$ at $x = l$ due to charge $4q$ at $x = 0$ is given

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$-q$

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(A) Let the positions of the charges be $x_1 = 0$,$x_2 = l/2$,and $x_3 = l$.The force on charge $q$ at $x = l$ due to charge $4q$ at $x = 0$ is given by Coulomb's Law:$F_1 = \frac{1}{4\pi\varepsilon_0} \cdot \frac{(4q)(q)}{l^2} = \frac{4q^2}{4\pi\varepsilon_0 l^2}$The force on charge $q$ at $x = l$ due to charge $Q$ at $x = l/2$ is:$F_2 = \frac{1}{4\pi\varepsilon_0} \cdot \frac{(Q)(q)}{(l/2)^2} = \frac{4Qq}{4\pi\varepsilon_0 l^2}$For the resultant force on $q$ to be zero,the sum of forces must be zero:$F_1 + F_2 = 0$$\frac{4q^2}{4\pi\varepsilon_0 l^2} + \frac{4Qq}{4\pi\varepsilon_0 l^2} = 0$$4q^2 + 4Qq = 0$$4Qq = -4q^2$$Q = -q$

Three charges $4q$,$Q$,and $q$ are placed in a straight line at positions $0$,$l/2$,and $l$ respectively. The resultant force on $q$ will be zero if $Q = $

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