Question

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 $K=\frac{1}{4\pi {\epsilon }_0}\frac{q}{L^2},$ which of the following statements(s) is(are) correct.

• A. The electric field at O is 6K along OD
• B. The potential at O is zero
• C. The potential at all points on the line PR is same
• D. The potential at all points on the line ST is same

Answer 1

Answer: (A), (B), (C)

(a) Resultant of 2K and 2K (at $120^{\circ }$) is also 2K towards
4A .Therefore, net electric field is 6A.
(b) $V_0=\frac{1}{4\pi {\epsilon }_0}[\frac{q_A}{L}+\frac{q_B}{L}+\frac{q_C}{L}+\frac{q_D}{L}+\frac{q_E}{L}+\frac{q_F}{L}]$
$=\frac{1}{4\pi {\epsilon }_0}(q_A+...+q_F)$
$=0$
Because $q_A+q_B+q_C+q_D+q_E+q_F=0$
(c) Only line PR. potential is same (= 0).