Electrostatics 2 Question 19
20. Six point charges are kept at the vertices of a regular hexagon of side $L$ and centre $O$ as shown in the figure. Given that $K=\frac{1}{4 \pi \varepsilon _0} \frac{q}{L^{2}}$, which
of the following statements(s) is(are) correct.
(2012)
(a) The electric field at $O$ is $6 K$ along $O D$
(b) The potential at $O$ is zero
(c) The potential at all points on the line $P R$ is same
(d) The potential at all points on the line $S T$ is same
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Solution:
- (a)
Resultant of $2 K$ and $2 K$ (at $120^{\circ}$ ) is also $2 K$ towards $4 K$.Therefore, net electric field is $6 K$.
$$ \begin{aligned} V _0 & =\frac{1}{4 \pi \varepsilon _0} \frac{q _A}{L}+\frac{q _B}{L}+\frac{q _C}{L}+\frac{q _D}{L}+\frac{q _E}{L}+\frac{q _F}{L} \\ & =\frac{1}{4 \pi \varepsilon _0 L}\left(q _A+\ldots+q _F\right)=0 \end{aligned} $$
Because $q _A+q _B+q _C+q _D+q _E+q _F=0$
(c) Only line PR, potential is same $(=0)$.
