The electric field at (3,3,-2) m due to 9.4 nC at(2, -2, 3) and -9.8 nC at (-3, 3, 1) is 0.28 N/C.
The electric field at the given position is determined from the summation of the field due to the two charges.
The electric field at (3,3,-2) m due to 9.4 nC at(2, -2, 3) is calculated as follows;
[tex]|r_1_2| = \sqrt{(2 -3)^2 + (-2-3)^2 + (3 --2)^2} = \sqrt{(1)^2 + (-5)^2 + (5)^2} \\\\|r_1_2|= 7.14 \ m[/tex]
[tex]E_{12} = \frac{kQ}{r^2} (\frac{3i + 3j - 2k}{|r|} )\\\\E_{12} = \frac{9\times 10^9 \times 9.4\times 10^{-9}}{7.14^2}(\frac{3i + 3j - 2k}{7.14} )\\\\E_1_2 = 0.23(3i + 3j - 2k)\\\\E_1_2 = 0.69i + 0.69j - 0.46k[/tex]
The electric field at (3,3,-2) m due to -9.4 nC at(-3,3,1) is calculated as follows;
[tex]|r_2_3| = \sqrt{(-3-3)^2 + (3-3)^2 + (1--2)^2 } \\\\|r_2_3| = 6.71 \ m[/tex]
[tex]E_{23} = \frac{kQ}{r^2} (\frac{3i + 3j - 2k}{|r|} )\\\\E_{23} = \frac{9\times 10^9 \times (-9.8\times 10^{-9})}{6.71^2}(\frac{3i + 3j - 2k}{6.71} )\\\\E_2_3 = -0.29(3i + 3j - 2k)\\\\E_2_3 = -0.87i - 0.87j + 0.58k[/tex]
E(12) + E(23) = -0.18i - 0.18j + 0.12k
[tex]|E| = \sqrt{(0.18)^2 + (0.18)^2 +(0.12)^2} \\\\|E| = 0.28 \ N/m[/tex]
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