Question

The positive point charges, each equal to +q, are placed at corners A, B and C of a square of side a. The magnitude of the force experienced by a point charge +Q placed at corner D is

• A. $\frac{3qQ}{4\pi {ϵ}_0{a}^2}$
• B. $\frac{\sqrt{2}qQ}{4\pi {ϵ}_0{a}^2}$
• C. $\frac{qQ}{4\pi {ϵ}_0{a}^2}(\sqrt{2}+\frac{1}{2})$
• D. Zero

Answer 1

The correct option is C

$\frac{qQ}{4\pi {ϵ}_0{a}^2}(\sqrt{2}+\frac{1}{2})$

Refer to Fig. 20.41 Forces $F_A,F_B$ and $F_C$ exerted on charge +Q by charges at A, B and C respectively are shown.
$F_A=F_C=\frac{1}{4\pi {ϵ}_0}.\frac{qQ}{a^2}and{F}_B=\frac{1}{4\pi {ϵ}_0}.\frac{qQ}{2a^2}$
F' is the resultant of $F_A$ and $F_C$.
F' by using the parallelogram of vector addition is:
F' = $\frac{\sqrt{2}qQ}{4\pi {ϵ}_0{a}^2}$

The net force on Q is $F"=F^{\prime }+F_B.$ It is to see that the correct choice is (c).