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The three charges \mathrm{q} / 2, \mathrm{q}$ and $\mathrm{q} / 2 are placed at the corners \mathrm{A}, \mathrm{B}$ and $\mathrm{C} of a square of side ' a 'as shown in figure. The magnitude of electric field (E) at the corner D of the square, is :

Option: 1

\frac{q}{4 \pi \epsilon_{0} a^{2}}\left(\frac{1}{\sqrt{2}}+\frac{1}{2}\right)


Option: 2

\frac{q}{4 \pi \in_{0} a^{2}}\left(1+\frac{1}{\sqrt{2}}\right)


Option: 3

\frac{q}{4 \pi \epsilon_{0} a^{2}}\left(1-\frac{1}{\sqrt{2}}\right)


Option: 4

\frac{\mathrm{q}}{4 \pi \epsilon_{0} \mathrm{a}^{2}}\left(\frac{1}{\sqrt{2}}-\frac{1}{2}\right)


Answers (1)

best_answer

\mathrm{\text { Let } \frac{k q}{2 a^{2}}=E} \\

\mathrm{E_{1}=E }\\

\mathrm{E_{2}=E} \\

\mathrm{E_{3}=\frac{k q^{2}}{2 a^{2}}=E }

\mathrm{\text { Enet } =E+\sqrt{2} E} \\

\mathrm{=(\sqrt{2}+1) \frac{k q}{2 a^{2}}} \\

\mathrm{=\frac{q}{4 \pi \varepsilon_{0} a^{2}}\left[\frac{\sqrt{2}}{2}+\frac{1}{2}\right]} \\

\mathrm{=\frac{q}{4 \pi \varepsilon_{0} a^{2}}\left[\frac{1}{\sqrt{2}}+\frac{1}{2}\right] }

Hence correct option is 1

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