Two electrostatic point charges of +60.0 uC and +50.c uC exert a repulsive force on each other of 175 N. What is the distance between the two charges?
So let's say I use Coulomb's law would the repulsion of 175 N be considered the equivalent of the electric force? Can someone please transform the formula of: electric force = coulomb constant * (charge 1)(charge 2)/ (distance )^2 so that the distance is in the left side? Sorry but I was never good at equations.
distance= sqrt(kq1q2/force)
3.9
Yes, you can use Coulomb's law to solve this problem. The repulsion of 175 N is indeed considered the equivalent of the electric force between the two charges.
To isolate the distance in the formula, we can rearrange Coulomb's law equation as follows:
Electric force = Coulomb constant * (charge 1 * charge 2) / (distance)^2
To solve for the distance, we can start by multiplying both sides of the equation by (distance)^2:
Electric force * (distance)^2 = Coulomb constant * (charge 1 * charge 2)
Next, divide both sides of the equation by the electric force:
(distance)^2 = Coulomb constant * (charge 1 * charge 2) / Electric force
Finally, take the square root of both sides of the equation to solve for the distance:
distance = √(Coulomb constant * (charge 1 * charge 2) / Electric force)
Substituting the values given:
distance = √((9 x 10^9 N m^2/C^2) * (60 x 10^-6 C * 50 x 10^-6 C) / 175 N)
Simplifying the expression:
distance = √(9 x 10^9 N m^2/C^2 * 3 x 10^-6 C^2 / 175 N)
distance = √((9 x 3) x 10^9 x 10^-6 C^2 m^2 / 175)
distance = √(27 x 10^3 m^2 / 175)
distance = √(154.29 m^2)
distance ≈ 12.43 meters (rounded to two decimal places)
Therefore, the distance between the two charges is approximately 12.43 meters.
Yes, you are correct. The repulsion force of 175 N can be considered as the electric force between the two charges. In order to rearrange the formula to isolate the distance, let's start with the original equation:
electric force = Coulomb constant * (charge 1) * (charge 2) / (distance)^2
To transform the formula so that the distance is on the left side, we can start by multiplying both sides of the equation by (distance)^2:
(electric force) * (distance)^2 = Coulomb constant * (charge 1) * (charge 2)
Next, we divide both sides of the equation by the electric force:
(distance)^2 = (Coulomb constant * (charge 1) * (charge 2)) / (electric force)
Finally, to solve for the distance, we take the square root of both sides of the equation:
distance = sqrt((Coulomb constant * (charge 1)*(charge 2)) / (electric force))
Now, you can substitute the values given in the problem statement into this formula to find the distance between the two charges.