Question

Three negative point charges - q each, and three positive point charges + q. + q and + Q are placed at the vertices of a regular hexagon as shown in Fig. 20.16. For what value of Q will the electric field at centre O due to the five charges at A, B, D, E and F be twice the electric field at centre O due to charge Q at C alone?

• A. q
• B. $\frac{q}{2}$
• C. 2q
• D. 5q

Answer 1

The correct option is B

$\frac{q}{2}$

The electric fields at centre O due to charges -q at A and D are equal and opposite. Hence they cancel each other. Similarly charges +q at B and E do not contribute to electric field at O. Dut to charge -q at F, the electric field at O will be
$E_1=\frac{q}{4\pi {ϵ}_0{r}^2}$ directed from O to F'
This is the net electric field at O due to the five charges at A,B,C,D,E and F. The electric field at O due to charge +Q at C is given by
$E_2=\frac{Q}{4\pi {ϵ}_0{r}^2}$ we require
$\frac{q}{4\pi {ϵ}_0{r}^2}=\frac{2Q}{4\pi {ϵ}_0{r}^2}$
which gives $Q=\frac{q}{2}$. Hence the correct choice is (b).