Question

two charges that each have a magnitude of 0.03 c are 10m away from each other. what is the force between them?

Explanation:

Step1: Recall Coulomb's law

Coulomb's law formula is \(F = k\frac{q_1q_2}{r^2}\), where \(k = 9\times10^{9}\space N\cdot m^{2}/C^{2}\), \(q_1 = q_2=0.03\space C\), and \(r = 10\space m\).

Step2: Substitute values into the formula

Substitute the values: \(F=9\times 10^{9}\times\frac{0.03\times0.03}{10^{2}}\).
First calculate \(0.03\times0.03 = 0.0009\), then \(\frac{0.0009}{100}=9\times10^{-6}\).
Then \(F = 9\times10^{9}\times9\times10^{-6}\).
Using the rule of exponents \(a^{m}\times a^{n}=a^{m + n}\), we have \(F=(9\times9)\times10^{9+( - 6)}\).
\(9\times9 = 81\), and \(9+( - 6)=3\), so \(F = 81\times10^{3}\space N\).

Answer:

\(8.1\times 10^{4}\space N\)