Calculating the Magnitude of Charges in MicroCoulombs

Calculation using Coulomb's Law

Two equal, but oppositely charged particles are attracted to each other electrically. The size of the force of attraction is 87.96 N when they are separated by 24.04 cm.

The magnitude of the electric force between two charged particles is given by Coulomb's Law:

\[F=k\frac{|q_1q_2|}{r^2}\]

Where \(q_1\) and \(q_2\) are the charges of the particles, \(r\) is the distance between the charged particles and \(k\) is the Coulomb's Constant:

\[k=8.99\times10^9N\frac{m^2}{C^2}\]

Since the magnitude of both charges is the same, the equation becomes:

\[F=\frac{kq^2}{r^2}\]

The force and the distance between the particles are given, the value of \(k\) is known and the charge \(q\) is unknown. Isolate \(q\) from the equation:

\[q=r\sqrt{\frac{F}{k}}\]

Replace the values of \(r=24.04\times10^{-2}m\), \(F=87.96N\) as well as the value of \(k\) to find the magnitude of the charges:

\[q=(24.04\times10^{-2}m)\times\sqrt{\frac{87.96N}{8.99\times10^9N\frac{m^2}{C^2}}}\]

\[q=23.78\mu C\]

Therefore, the magnitude of the charges in microCoulombs is: 23.78μC.