two charges attract each other with a force of 2.5 N. What will be the force if the distance between them is reduced to one-ninth its orginal value?
To determine the new force between the charges when the distance is reduced, we can 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.
The formula for Coulomb's Law is:
F = (k * q1 * q2) / r^2
Where:
F = Force between charges
k = Coulomb's constant (k = 9 * 10^9 N m^2/C^2)
q1, q2 = Magnitudes of the charges
r = Distance between the charges
In this case, the original force is 2.5 N. Let's denote the original distance between the charges as r1. The new distance after reducing it to one-ninth its original value is r2 = r1/9.
To find the new force, we need to find the new distance between the charges and substitute it into the Coulomb's Law equation.
1. Determine the new distance between the charges (r2):
r2 = r1 / 9
2. Calculate the new force (F2) using Coulomb's Law:
F2 = (k * q1 * q2) / (r2^2)
Substituting the values into the equation, we have:
F2 = (k * q1 * q2) / ((r1/9)^2) = (k * q1 * q2) / ((r1^2)/81)
Simplifying further, we get:
F2 = (k * q1 * q2 * 81) / (r1^2)
Now, we can calculate the new force (F2) by multiplying the original force (2.5 N) by 81 and dividing by the square of the original distance (r1):
F2 = (2.5 N * 81) / (r1^2)
Therefore, to find the new force when the distance is reduced to one-ninth its original value, multiply the original force by 81 and divide by the square of the original distance.