Two point charges are 10 cm apart and their combined charge is 9μC. Ifthey repel each other with a force of 18N, then calculate the magnitude ofeach charge

Sure, let's solve this step by step.

Step 1: Understand the problem We have two point charges that are 10 cm apart. They repel each other with a force of 18N. The combined charge is 9μC. We need to find the magnitude of each charge.

Step 2: Use Coulomb's Law Coulomb's Law states that the force between two charges is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. Mathematically, it is represented as:

F = k * |q1*q2| / r^2

where: F is the force between the charges, k is Coulomb's constant (9 * 10^9 N.m^2/C^2), q1 and q2 are the charges, r is the distance between the charges.

Step 3: Set up the equations Let's denote the charges as q1 and q2. We know that q1 + q2 = 9μC = 9 * 10^-6 C (since 1μC = 10^-6 C). We also know from Coulomb's Law that:

18N = 9 * 10^9 N.m^2/C^2 * |q1q2| / (10cm)^2 = 9 * 10^9 N.m^2/C^2 * |q1q2| / (0.1m)^2

Step 4: Solve the equations We now have a system of two equations, which we can solve to find the values of q1 and q2. However, this is a quadratic equation system, and it might be a bit complex to solve.

The solution to this system will give the magnitudes of the two charges.