Understanding Coulomb's Law: Calculating Forces Between Charged Particles

Coulomb's law is a fundamental principle in physics that describes the force between two point charges. This law is crucial in understanding the behavior of charged particles in various physical phenomena. Let's explore the concept in detail and calculate the force between two specific charges using Coulomb's law formula.

Coulomb's Law Formula

The formula for Coulomb's law is given as:

F k frac{q_1 q_2}{r^2}

Where:

F is the magnitude of the force between the charges. k is Coulomb's constant, approximately 8.99 times 10^9 frac{N m^2}{C^2}. q_1 and q_2 represent the amounts of the charges in Coulombs (C). r is the distance between the charges in meters (m).

Calculating the Force Between 3C and -4C Charges Separated by 10m

Let's consider two charges: a positive charge q_1 3 text{C} and a negative charge q_2 -4 text{C}, which are separated by a distance of r 10 text{m}.

Substituting these values into the Coulomb's law formula:

F 8.99 times 10^9 frac{(3)(-4)}{10^2}

To find the absolute value of the product of the charges:

3 times -4 -12

Substituting this value back into the equation:

F 8.99 times 10^9 frac{-12}{100}

F 8.99 times 10^9 times -0.12

F -1.0788 times 10^9 text{N}

The force is approximately -1.08 billion newtons.

Since one charge is positive and the other is negative, the force is attractive.

Interpreting the Sign and Nature of the Force

In Coulomb's law, if the calculated force F is negative, it indicates an attractive force. Conversely, if the force is positive, it indicates a repulsive force. This is a direct result of the signs of the charges involved.

For example, if we substitute the values into the formula again:

F 9 times 10^9 frac{(3)(-4)}{10^2} -1 times 10^9 text{N}

Since the sign of the force is negative, it confirms that the force is attractive, as expected when dealing with opposite charges.

Conclusion

Understanding Coulomb's law is vital for comprehending the interactions between charged particles. By following the formula and steps, we can calculate the force between any two charges. In this case, the force between a 3C charge and a -4C charge separated by 10 meters is approximately -1.08 billion newtons, indicating an attractive force.