The sum of two point charges is 7 μC. They repel each other with aforce of 1 N when kept 30 cm apart in free space. Calculate the value ofeach charge.2

To solve this problem, we can use Coulomb's Law, which 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. The formula for Coulomb's Law is:

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, and r is the distance between the charges.

Given: F = 1 N, r = 30 cm = 0.3 m, and q1 + q2 = 7 μC = 7 * 10^-6 C.

We can assume q1 = x and q2 = 7 * 10^-6 - x.

Substituting these values into Coulomb's Law gives us:

1 = 9 * 10^9 * x * (7 * 10^-6 - x) / (0.3)^2

Solving this quadratic equation will give us the values of x, which represent the values of the two charges.

The solutions to this equation are x = 5 * 10^-6 C and x = 2 * 10^-6 C.

So, the two charges are 5 μC and 2 μC.