Question

Point charges of $3 \times 10^{-9}\,C$ situated at each of three comers of a square whose side is 15 cm. The magnitude and direction of A electric field at the vacant corner of the square is

• A. 2296 y/m along the diagonal
• B. 9622 V/m along the diagonal
• C. 22.0 V/m along the diagonal
• D. zero

Answer 1

Answer: (A)

Effective electric field will be $\sqrt{2} E _{1}+ E _{2}$ along the diagonal.
$\Rightarrow E =\frac{ kq _{1}}{\left(15 \times 10^{-2}\right)^{2}} \sqrt{2}+\frac{ kq _{1}}{\left(\sqrt{2} \times 15 \times 10^{-2}\right)^{2}}$
$=\frac{9 \times 10^{9} \times 3 \times 10^{-9} \times \sqrt{2}}{225 \times 10^{-4}}+\frac{9 \times 10^{-9} \times 3 \times 10^{-9}}{2 \times 225 \times 10^{-4}}$
$=\frac{38.1}{225 \times 10^{-4}}+\frac{13.5}{225 \times 10^{-4}}$
$=\frac{51.6}{225 \times 10^{-4}}$
$ E =2293.33 \,V / m $
$=2294 \,V / m $