If four charges q_1 = +1 times 10^{-8} text{ | vedclass

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(C) Given charges at the corners of a square of side $a = 1 	ext{ m}$ are:$q_1 = +1 	imes 10^{-8} 	ext{ C}$$q_2 = -2 	imes 10^{-8} 	ext{ C}$$q_3

Vedclass · Accepted Answer

$510$

Vedclass · Answer

(C) Given charges at the corners of a square of side $a = 1 	ext{ m}$ are:$q_1 = +1 	imes 10^{-8} 	ext{ C}$$q_2 = -2 	imes 10^{-8} 	ext{ C}$$q_3 = +3 	imes 10^{-8} 	ext{ C}$$q_4 = +2 	imes 10^{-8} 	ext{ C}$The distance $r$ from each corner to the centre of the square is half the diagonal length:$r = \frac{\sqrt{2}a}{2} = \frac{a}{\sqrt{2}} = \frac{1}{\sqrt{2}} 	ext{ m}$The electric potential $V$ at the centre is the algebraic sum of the potentials due to each charge:$V = \frac{k q_1}{r} + \frac{k q_2}{r} + \frac{k q_3}{r} + \frac{k q_4}{r} = \frac{k}{r} (q_1 + q_2 + q_3 + q_4)$Substituting the values:$V = \frac{9 	imes 10^9}{1/\sqrt{2}} (1 - 2 + 3 + 2) 	imes 10^{-8}$$V = 9 \sqrt{2} 	imes 10^1 	imes (4)$$V = 36 \sqrt{2} 	imes 10 \approx 36 	imes 1.414 	imes 10 = 509.04 	ext{ V}$Rounding to the nearest given option, $V \approx 510 	ext{ V}$.

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