Three charges 4q,,Q and q are in a straight l | vedclass

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Question

(a) The force between $4q$ and $q$; ${F_1} = \frac{1}{{4\pi {\varepsilon _0}}} \cdot \frac{{4q 	imes q}}{{{l^2}}}$
The force between $Q$ and $q$; ${

Vedclass · Accepted Answer

$-q$

Vedclass · Answer

(a) The force between $4q$ and $q$; ${F_1} = \frac{1}{{4\pi {\varepsilon _0}}} \cdot \frac{{4q 	imes q}}{{{l^2}}}$
The force between $Q$ and $q$; ${F_2} = \frac{1}{{4\pi {\varepsilon _0}}} \cdot \frac{{Q 	imes q}}{{{{(l/2)}^2}}}$
We want ${F_1} + {F_2} = 0$ or $\frac{{4{q^2}}}{{{l^2}}} = - \frac{{4Qq}}{{{l^2}}}$ $==>$ $Q = - q$

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

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