Question

Two point charges (+Q) and (– 2Q) are fixed on the X-axis at positions a and 2a from origin respectively. At what position on the axis, the resultant electric field is zero

• A. Only $x = \sqrt{2}a$
• B. Only $x = - \sqrt{2}a$
• C. Both $x = \pm \sqrt{2}a$
• D. $x = \frac{3a}{2}$ only

Answer 1

Answer: (C)

Both $x = \pm \sqrt{2}a$

Answer 2

Initially, force between A and C $F = k\frac{Q^{2}}{r^{2}}$

When a similar sphere B having charge +Q is kept at the mid point of line joining A and C, then Net force on B is

$F_{net} = F_{A} + F_{C} = k\frac{Q^{2}}{\left( \frac{r}{2} \right)^{2}} + \frac{kQ^{2}}{\left( \frac{r}{2} \right)^{2}} = 8\frac{kQ^{2}}{r^{2}} = 8F$.(Direction is shown in figure)