Six point charges each of the magnitude $Q$ are placed at the vertices of a regular hexagon of side $a$ as shown in the figure. Electric field intensity on the line passing through the centre $O$ and perpendicular to the plane of the figure at a large distance $x(\gg > a)$ from $O$ is $\left(\text {Let, } \frac{1}{4 \pi \in_0}=k\right)$

Question

Aicharya · Accepted Answer

According to the question, Let $O K=x$ due to $A B$, force at the point $K$ is only along $A B$ $\text {i.e., } F_K=\frac{2 k Q a}{\left(a^2+x^2\right)^{\frac{3}{2}}}$ $\therefore$ There are three such $F_K^{\prime} s$ so the net resultant of these three, $\begin{aligned} & F_{\text {net }}=\frac{4 k Q a}{\left(a^2+x^2\right)^{\frac{3}{2}}}=\frac{4 k Q a}{x^3\left(1+\frac{a^2}{x^2}\right)^{\frac{3}{2}}} \ & F_{\text {net }}=\frac{4 k Q a}{x^3} \quad\left(\therefore \frac{a^2}{x^2}=0\right),(x > > a) \end{aligned}$

Six point charges each of the magnitude \(Q\) are placed at the vertices of a regular hexagon of side \(a\)…

Solution