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 two point charges is 7μC and they repel each other with a force of 1N when kept 30cm apart in free space. 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. It is given by the formula:

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 amounts of charge, r is the distance between the charges.

Step 3: Set up the equations We know that q1 + q2 = 7μC = 7 * 10^-6 C (since 1μC = 10^-6 C). Let's call this Equation 1.

From Coulomb's law, we have 1N = 9 * 10^9 * q1 * q2 / (0.3)^2. Let's call this Equation 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. This involves some algebra and possibly the use of the quadratic formula.

Note: Since the charges repel each other, both must have the same sign. Therefore, both q1 and q2 must be positive.