A +5 microcoulomb charge experiences a .55 N force in the positive y direction. If this charge is replaced with a -2.7 microcoulomb charge, find the magnitude of the force in this case.
The force magnitude will get multiplied by a factor 2.7/5 = 0.54, making it 0.297 N, and the direction will reverse
To find the magnitude of the force on a charge, you can use Coulomb's Law. Coulomb's Law states that the magnitude of the force between two charges is directly proportional to the product of the magnitudes of the 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 magnitude of the force, q1 and q2 are the magnitudes of the charges, r is the distance between the charges, and k is the electrostatic constant.
In this case, you are given a charge of +5 microcoulombs experiencing a force of 0.55 N in the positive y direction. So, let's calculate the magnitude of the force between the given charge and the charge it interacts with:
First, convert the charges from microcoulombs to coulombs:
q1 = +5 * 10^-6 C
q2 = -2.7 * 10^-6 C
Now, plug the values into the formula:
F1 = k * (q1 * q2) / r^2
Solving for F1:
F1 = (9 * 10^9 N * m^2 / C^2) * (|+5 * 10^-6 C| * |-2.7 * 10^-6 C|) / r^2
Next, calculate the magnitude of the force:
F1 = (9 * 10^9 N * m^2 / C^2) * (5 * 10^-6 C * 2.7 * 10^-6 C) / r^2
With the given information, you can now solve for the magnitude of the force when the charge is replaced with a -2.7 microcoulomb charge.