Two positive charges of +2 coulombs are 3 meters apart. If one of the charges is replaced by the negative charge -2 coulombs, the magnitude of force between them is:
a)larger b)smaller c)the same
d)zero e)none of these
To determine the magnitude of the force between charges, we can use Coulomb's law. Coulomb's law states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Let's calculate the force between the two positive charges using Coulomb's law. Assuming the charges are point charges, the equation can be written as:
F = k * (q1 * q2) / r^2
Where:
F is the magnitude of the force between the charges,
k is the electrostatic constant, approximately equal to 9 × 10^9 N m^2/C^2,
q1 and q2 are the magnitudes of the charges, and
r is the distance between the charges.
Given:
q1 = +2 C (positive charge)
q2 = +2 C (positive charge)
r = 3 m
Substituting these values into the equation:
F = (9 × 10^9 N m^2/C^2) * (+2 C * +2 C) / (3 m)^2
Simplifying:
F = (9 × 10^9 N m^2/C^2) * (4 C^2) / 9 m^2
F = 4 N
Therefore, the magnitude of the force between the two positive charges is 4 Newton.
Now, let's replace one of the positive charges with a negative charge of -2 C. The new configuration has a positive charge of +2 C and a negative charge of -2 C, separated by 3 m.
Using Coulomb's law again to calculate the force with the new configuration:
F' = (9 × 10^9 N m^2/C^2) * (+2 C * -2 C) / (3 m)^2
F' = (9 × 10^9 N m^2/C^2) * (-4 C^2) / 9 m^2
F' = -4 N
Thus, the magnitude of the force between the charges after replacing one of them with the negative charge is 4 Newton, but with an opposite direction. So, the answer is c) the same.