By what distance must two charges of +2 C and +4 C be separated so that the repulsive force between them is 4.10 1010 N?
To find the distance between two charges, we can use Coulomb's Law, which states that the electrostatic force of attraction or repulsion between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.
Coulomb's Law formula:
F = (k * |Q1 * Q2|) / r^2
Where:
F is the force between the charges in Newtons (N).
k is Coulomb's constant, approximately equal to 9 x 10^9 Nm^2/C^2.
Q1 and Q2 are the magnitudes of the charges in Coulombs (C).
r is the distance between the charges in meters (m).
In this problem, we are given:
Q1 = +2 C
Q2 = +4 C
F = 4.10 x 10^10 N
Let's substitute these values into the formula and solve for r:
4.10 x 10^10 N = (9 x 10^9 Nm^2/C^2 * |2 C * 4 C|) / r^2
First, simplify the numerator:
(9 x 10^9 Nm^2/C^2 * 8 C^2) / r^2 = 4.10 x 10^10 N
Cancel out the units:
(72 x 10^9 Nm^2) / r^2 = 4.10 x 10^10 N
Simplify the equation:
72 / r^2 = 4.10 x 10
Multiply both sides by r^2:
72 = (4.10 x 10) * r^2
Divide both sides by (4.10 x 10):
72 / (4.10 x 10) = r^2
Evaluate the left side:
17.56 = r^2
Next, take the square root of both sides to get the value of r:
r = √17.56
Using a calculator, we find that r ≈ 4.19 m.
Therefore, the two charges of +2 C and +4 C must be separated by approximately 4.19 meters for the repulsive force between them to be 4.10 x 10^10 N.
Coulomb’s Law
F = k •q1•q2/r^2,
k =9•10^9 N•m^2/C^2,
r =sqrt{ k •q1•q2/F}