Question 719: Electrostatics & Capacitance

Question

Six charges +q, $-$q, +q, $-$q, +q, and $-$q are fixed at the corners of a hexagon of side d as shown in the figure. The work done in bringing a charge q
0
to the centre of the hexagon from infinity is
(${\varepsilon _0}$ - permittivity of free space)
![](https://app-content.cdn.examgoal.net/fly/@width/image/1lab1ou1m/353aab65-7a4d-4e70-9b20-d9aa0a5ef442/02a5e7a0-60f3-11ed-b81b-f1e44e9e12b2/file-1lab1ou1n.png?format=png)

Accepted Answer

Work done $ = {q_0}\,.\,({V_0} - {V_\infty })$
$ = \left\{ {{{3kq} \over d} + \left( {{{ - 3kq} \over d}} \right)} \right\}{q_0}$
= Zero
![](https://app-content.cdn.examgoal.net/fly/@width/image/1lab1q869/6abc130a-e120-46c2-98bd-ff72c9fcdf70/295f1510-60f3-11ed-b81b-f1e44e9e12b2/file-1lab1q86a.png?format=png)

Answer

${{ - {q^2}} \over {4\pi {\varepsilon _0}d}}\left( {6 - {1 \over {\sqrt 2 }}} \right)$

Answer

Zero

Answer

${{ - {q^2}} \over {4\pi {\varepsilon _0}d}}$

Answer

${{ - {q^2}} \over {4\pi {\varepsilon _0}d}}\left( {3 - {1 \over {\sqrt 2 }}} \right)$

Electrostatics & Capacitance

Six charges +q, -q, +q, -q, +q, and -q are fixed at the corners of a hexagon of side d as shown in the figure. The work done in bringing a charge q 0 to the centre of the hexagon from infinity is ({\varepsilon _0} - permittivity of free space)

Choose the correct answer: