Answer:
200 C
Explanation:
Let C1 and C2 be their charges. According to Coulomb's law
[tex]F_C = k\frac{C_1C_2}{R^2}[/tex]
where k = [tex]8.99\times10^9 nm^2/C^2[/tex] is the constant, R = 0.4m is the distance between them, F = 120 N is their resulting charge force
[tex]120 = 8.99\times10^9\frac{C_1C_2}{0.4^2}[/tex]
[tex]C_1C_2 = \frac{120*0.4^2}{8.99\times10^9} = 2.13\times10^{-9}[/tex]
Since their total charge is 200C:
[tex]C_1 + C_2 = 200[/tex] or [tex]C_1 = 200 - C_2[/tex]
We can substitute the above equation
[tex]C_1C_2 = (200 - C_2)C_2 = 2.13\times10^{-9}[/tex]
[tex]-C_2^2 +200C_2 - 2.13\times10^{-9} = 0[/tex]
[tex]C= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}[/tex]
[tex]C= \frac{-200\pm \sqrt{(200)^2 - 4*(-1)*(-0.00000000213)}}{2*(-1)}[/tex]
[tex]C= \frac{-200\pm200}{-2}[/tex]
[tex]C = 1.06 \times 10^{-11}[/tex] or [tex]C \approx 200[/tex]
So the larger charge is C = 200 C
