Two point charges are separated by 6cm. The attractive force between them is 22 N. Find the force between them when they are separated by 12 cm.
force is inversely proportional to the square of distance. Double distance, force is now 1/4th what it was.
To find the force between two point charges when they are separated by a different distance, you can use Coulomb's Law.
Coulomb's Law states that the force, F, between two point charges, q1 and q2, separated by a distance, r, is given by the equation:
F = k * (q1 * q2) / r^2,
where k is the electrostatic constant, which has a value of 9 * 10^9 N m^2/C^2.
In this case, we are given that the force between the two charges is 22 N when they are separated by a distance of 6 cm (which is equivalent to 0.06 m).
Plugging these values into the formula, we can solve for the product of the charges, q1 * q2:
22 N = (9 * 10^9 N m^2/C^2) * (q1 * q2) / (0.06 m)^2.
To find the force when the charges are separated by a distance of 12 cm (which is equivalent to 0.12 m), we can use the same equation and solve for the force, F, with the new distance, r:
F = (9 * 10^9 N m^2/C^2) * (q1 * q2) / (0.12 m)^2.
Now, we can solve for the new force. First, let's rearrange the equation to solve for q1 * q2:
(q1 * q2) = (22 N * (0.06 m)^2) / (9 * 10^9 N m^2/C^2).
And then, we can substitute this value back into the equation to find the new force:
F = (9 * 10^9 N m^2/C^2) * [(22 N * (0.06 m)^2) / (q1 * q2)] / (0.12 m)^2.
By solving this equation, we can determine the force between the two charges when they are separated by 12 cm.