Question #295137

Four charges, q_{1} = 5.00 * 10 ^ - 7 * C q_{2} = - 3.00 * 10 ^ - 7 * C , q_{3} = - 2.00 * 10 ^ - 7 * C and q 4 =6.00* 10 ^ - 7 * t , are situated at the corners of a square if side 4.00 m. Find the potential at the center of the square.



Given: q_{1} = 5.00 * 10 ^ - 7 * c


q_{2} = - 3.00 * 10 ^ - 7 * C


q_{3} = - 2.00 * 10 ^ - 7 * C


q_{4} = 6.00 * 10 ^ - 7 * C


1
Expert's answer
2022-02-14T14:38:48-0500

We know that

V1=kq1rV=9×109×5×10722=1590.99VV_1=\frac{kq_1}{r}\\V=\frac{9\times10^9\times5\times10^{-7}}{2\sqrt{2}}=1590.99V

V2=kq2rV=9×109×(3)×10722=954.59VV_2=\frac{kq_2}{r}\\V=\frac{9\times10^9\times(-3)\times10^{-7}}{2\sqrt{2}}=-954.59V

V3=kq3rV=9×109×(2)×10722=636.39VV_3=\frac{kq_3}{r}\\V=\frac{9\times10^9\times(-2)\times10^{-7}}{2\sqrt{2}}=-636.39V

V4=kq4rV=9×109×6×10722=1909.18VV_4=\frac{kq_4}{r}\\V=\frac{9\times10^9\times6\times10^{-7}}{2\sqrt{2}}=1909.18V

V=V1+V2+V3+V4V=V_1+V_2+V_3+V_4


V=1590.99954.59636.39+1909.18=1909.19VV=1590.99-954.59-636.39+1909.18=1909.19V


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