Answer:
c) [tex]4.2*10^{-5}C[/tex]
Explanation:
Coulomb's law says that the force exerted between two charges is inversely proportional to the square of distance between them, and is given by the expression:
[tex]F=\frac{kq_{1}q_{2}}{r^{2}}[/tex]
where k is a proportionality constant with the value [tex]k=9*10^{9}\frac{Nm^{2}}{C^{2}}[/tex]
In this case [tex]q_{1}=q_{2}=q[/tex], so we have:
[tex]F=\frac{kq^{2}}{r^{2}}[/tex]
Solving the equation for q, we have:
[tex]kq^{2}=Fr^{2}[/tex]
[tex]q^{2}=\frac{Fr^{2}}{k}[/tex]
[tex]q=\sqrt{\frac{Fr^{2}}{k}}[/tex]
Replacing the given values:
[tex]q=\sqrt{\frac{4.0N*(2.0m)^{2}}{9*10^{-9}\frac{Nm^{2}}{C^{2}}}}[/tex]
[tex]q=4.2*10^{-5}C[/tex]
