The sum of two point charges is 7μC. They repel each other with a force of 1N when kept 30cm apart in free space. Calculate the value of each charge.

Sure, let's solve this step by step.

Step 1: Understand the problem We know that the sum of the two charges is 7μC and they repel each other with a force of 1N when kept 30cm apart. We need to find the value 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 can be expressed 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 = 7μC = 7 * 10^-6 C (since 1μC = 10^-6 C). We also know that the force F = 1N. Substituting these values into Coulomb's law gives us:

1 = 9 * 10^9 * q1 * q2 / (0.3)^2

Step 4: Solve the equations We now have a system of two equations. To solve it, we can express q2 from the first equation (q2 = 7 * 10^-6 - q1) and substitute it into the second equation. After solving this equation for q1, we can find q2 using the first equation.

This is a quadratic equation, and solving it will give us the values of q1 and q2.