Question

problem 5
a force of 15 n exist between two positive charges ( q_1 = 7\times10^{-6}c ) and ( q_2 = 9\times10^{-6} ). the two charges are separated by an unknown ( d ). determine this unknown distance ( d ).
given that ( k = 9.0\times10^{9}n.m^{2}/c^{2} ).

Explanation:

Step1: Write Coulomb's Law formula

Coulomb's Law is \(F = k\frac{Q_1Q_2}{d^{2}}\). We need to solve for \(d\). Rearranging the formula for \(d\) gives \(d^{2}=k\frac{Q_1Q_2}{F}\), so \(d=\sqrt{k\frac{Q_1Q_2}{F}}\).

Step2: Substitute the given values

Substitute \(k = 9.0\times10^{9}\space N\cdot m^{2}/C^{2}\), \(Q_1 = 7\times 10^{-6}\space C\), \(Q_2=9\times 10^{-6}\space C\) and \(F = 15\space N\) into the formula:

$$
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Step3: Calculate the value of \(d\)

\(d\approx0.194\space m\)

Answer:

\(d\approx0.194\space m\)