Question

Four equal charges, each +q are placed on the four corners of a square of side a. Then the coulomb force experienced by one charge due to the rest of three is - $\left( K = \frac{1}{4\pi\varepsilon_{0}} \right)$

• A. $(2\sqrt{2} + 1)Kq^{2}/2a^{2}$
• B. 3Kq²/a²
• C. 2$\sqrt{2}$Kq²/a²
• D. Zero

Answer 1

Answer: (A)

$(2\sqrt{2} + 1)Kq^{2}/2a^{2}$

Answer 2

F₁₂ = F₁₄ = $\frac { \mathrm { kq } ^ { 2 } } { \mathrm { a } ^ { 2 } }$

Resultant of F₁₂ & F₁₄

= $\sqrt { \mathrm { F } _ { 12 } ^ { 2 } + \mathrm { F } _ { 14 } ^ { 2 } }$

= $\sqrt { \mathrm { F } _ { 12 } ^ { 2 } + \mathrm { F } _ { 12 } ^ { 2 } }$

= $\mathrm { F } _ { 12 } \sqrt { 2 }$

\ Net force on

charge q is

F = $\mathrm { F } _ { 12 } \sqrt { 2 }$ + F₁₃

= $\frac { \mathrm { kq } ^ { 2 } } { \mathrm { a } ^ { 2 } } \sqrt { 2 }$ +.