Answer:
[tex]q_1 = 6.22 \times 10^{-11} C[/tex]
[tex]q_2 = -6.22 \times 10^{-11} [/tex]
Explanation:
Force on the charge Q = -1.85 mC is along the line joining the two charges
so here we can say that net force on it is given by
[tex]F = ma[/tex]
[tex]F = (0.00550)(314)[/tex]
[tex]F = 1.727 N[/tex]
Now this is the force due to two charges which are in same magnitude but opposite sign
so this force is given as
[tex]F = 2\frac{kq_1q}{r^2} cos\theta[/tex]
here we know that
[tex]F = 2\frac{(9\times 10^9)(1.85 \times 10^{-3})(q)}{0.03^2}cos\theta[/tex]
here we know that
[tex]cos\theta = \frac{2.25}{3} = 0.75[/tex]
now we have
[tex]1.727 = 2\frac{(9\times 10^9)(1.85 \times 10^{-3})(q)}{0.03^2}(0.75)[/tex]
[tex]1.727 = 2.775 \times 10^{10} q[/tex]
[tex]q = 6.22 \times 10^{-11} C[/tex]
The values of charge 1 and charge 2 are [tex]q_{1}=9.30 \times 10^{-11} \;\rm C[/tex] and [tex]q_{2} = 2.10 \times 10^{-10} \;\rm C[/tex] respectively.
Given data:
The distance between the charges is, d = 4.50 cm = 0.045 m.
The magnitude of third charge is, [tex]Q=-1.85 \; \rm mC=-1.85 \times 10^{-3} \;\rm C[/tex].
The mass of third charge is, m = 5.50 g = 0.00550 kg.
The distance of third charge from other charges is, d' = 3.00 cm = 0.03 m.
The acceleration of third charge is, [tex]a=314 \;\rm m/s^{2}[/tex].
The force on third charge due to other charges is,
[tex]F = ma\\F=0.00550 \times 314\\F = 1.727 \;\rm N[/tex]
Since, the above force is of same in magnitude but opposite to electrostatic force on charge [tex]q_{1}[/tex] and [tex]q_{2}[/tex]
Therefore,
[tex]F=-F'\\F= -(k\dfrac{Q \times q_{1}}{d'^{2}}) \\\\1.727= -(9 \times 10^{9} \times \dfrac{-1.85 \times 10^{-3}\times q_{1}}{0.03^{2}})\\\\ q_{1}=9.30 \times 10^{-11} \;\rm C[/tex]
The force between the third charge and second charge is,
[tex]F = -F''\\1.727=-\dfrac{k \times Q \times q_{2}}{d^{2}}\\\\1.727=-\dfrac{9 \times 10^9 \times -1.85 \times 10^{-3} \times q_{2}}{0.045^{2}}\\\\q_{2} = 2.10 \times 10^{-10} \;\rm C[/tex]
Thus, the values of charge 1 and charge 2 are [tex]q_{1}=9.30 \times 10^{-11} \;\rm C[/tex] and [tex]q_{2} = 2.10 \times 10^{-10} \;\rm C[/tex] respectively.
Learn more about the electrostatic force here:
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