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Two point charges $\;q_{1}\;and\;q_{2}\;$ are placed on $\;x=-a\;and\;x=+a\;respectively\;.$ Find the relation between $\;q_{1}\;and\;q_{2}\;$ so that the net electric field at $\;x=+\large\frac{a}{2}\;$ is zero

$(a)\;q_{1}=q_{2}\qquad(b)\;q_{1}=9 q_{2}\qquad(c)\;q_{2}=9 q_{1}\qquad(d)\;none$

Answer : $\;q_{1}=9 q_{2}$
Explanation : $\;\large\frac{kq_{1}}{r^{2}_{1}}=\large\frac{kq_{2}}{r^{2}_{2}}$
$\;\large\frac{kq_{1}}{r^{2}_{1}}=\large\frac{kq_{2}}{r^{2}_{2}}$
Explanation : $\;\large\frac{kq_{1}}{r^{2}_{1}}=\large\frac{kq_{2}}{r^{2}_{2}}$
$\large\frac{kq_{1}}{(\large\frac{3a}{2})^2}=\large\frac{kq_{2}}{(\large\frac{a}{2})^2}$
$\large\frac{q_{1}}{9}=q_{2}$
$q_{1}=9 q_{2}\;.$

edited Aug 11, 2014