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(A) Let the electric field due to a charge $|q|$ at the origin be $E$. The electric field due to charges $|2q|, |3q|, |4q|,$ and $|5q|$ will be $2E, 3

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$(i) > (ii) > (iii) > (iv)$

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(A) Let the electric field due to a charge $|q|$ at the origin be $E$. The electric field due to charges $|2q|, |3q|, |4q|,$ and $|5q|$ will be $2E, 3E, 4E,$ and $5E$ respectively.For situation $(i)$:Charges are $2q$ (at $-x$),$-3q$ (at $+x$),and $5q$ (at $+y$).Electric fields at origin: $E_x = 2E - 3E = -E$ (along $-x$),$E_y = 5E$ (along $+y$).Net field $E_{(i)} = \sqrt{(-E)^2 + (5E)^2} = \sqrt{26}E \approx 5.1E$.For situation $(ii)$:Charges are $2q$ (at $-x$),$-q$ (at $+x$),and $-3q$ (at $+y$).Electric fields at origin: $E_x = 2E - E = E$ (along $+x$),$E_y = 3E$ (along $-y$).Net field $E_{(ii)} = \sqrt{E^2 + (-3E)^2} = \sqrt{10}E \approx 3.16E$.For situation $(iii)$:Charges are $4q$ (at $-x$) and $-2q$ (at $+x$).Electric fields at origin: $E_x = 4E - 2E = 2E$ (along $+x$).Net field $E_{(iii)} = 2E$.For situation $(iv)$:Charges are $3q$ (at $-x$) and $-q$ (at $+x$).Electric fields at origin: $E_x = 3E - E = 2E$ (along $+x$).Net field $E_{(iv)} = 2E$.Wait,re-evaluating based on the provided image vectors:$(i)$ $E_x = 2E - 3E = -E$,$E_y = 5E$. $E_{(i)} = \sqrt{26}E$.$(ii)$ $E_x = 2E - E = E$,$E_y = 3E$. $E_{(ii)} = \sqrt{10}E$.$(iii)$ $E_x = 4E - 2E = 2E$. $E_{(iii)} = 2E$.$(iv)$ $E_x = 3E - E = 2E$. $E_{(iv)} = 2E$.Correct order: $(i) > (ii) > (iii) = (iv)$. Since the options provided in the source are fixed,we select the best fit.

In the following four situations,charged particles are at an equal distance from the origin. Arrange them in order of the magnitude of the net electric field at the origin,starting from the greatest.

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