The coordinate of zero electric field of the two charges is (9.4 cm, 34.6 cm).
The electric field strength of a charge is defined as force per unit charge.
[tex]E= \frac{kq}{r^2} \\\\E = \frac{kq_1}{(x -6)^2} - \frac{kq_2}{(12 -x)^2} =0\\\\[/tex]
At zero net electric field, the electric field of the two charges will be equal.
Let the point of zero electric field = x
[tex]\frac{9 \times 10^9 \times 8 \times 10^{-12}}{(x -6)^2} - \frac{9 \times 10^9 \times 5 \times 10^{-12} }{(12 -x)^2} =0\\\\\frac{0.072}{x^2-12x + 36} - \frac{0.045}{144 -24x + x^2} =0\\\\0.045(x^2 -12x + 36) = 0.072(144-24x + x^2)\\\\0.045x^2 - 0.54x + 1.62= 10.368 - 1.728x + 0.072x^2\\\\0.027x^2 -1.188x + 8.748 = 0\\\\x = 9.4 \ cm, \ or \ 34.6\ cm[/tex]
Thus, the coordinate of zero electric field of the two charges is (9.4 cm, 34.6 cm).
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