Answer to Question #295137 in Electricity and Magnetism for cols

Question

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

Answer 1

We know that

$V_1=\frac{kq_1}{r}\\V=\frac{9\times10^9\times5\times10^{-7}}{2\sqrt{2}}=1590.99V$

$V_2=\frac{kq_2}{r}\\V=\frac{9\times10^9\times(-3)\times10^{-7}}{2\sqrt{2}}=-954.59V$

$V_3=\frac{kq_3}{r}\\V=\frac{9\times10^9\times(-2)\times10^{-7}}{2\sqrt{2}}=-636.39V$

$V_4=\frac{kq_4}{r}\\V=\frac{9\times10^9\times6\times10^{-7}}{2\sqrt{2}}=1909.18V$

$V=V_1+V_2+V_3+V_4$

$$V=1590.99-954.59-636.39+1909.18=1909.19V$$