A negative charge of − 2.0 μC and a positive charge of + 3.0 μC are separated by 8 cm. What is the force between the two charges?
To find the force between two charges, we can use Coulomb's Law. Coulomb's Law states that the force between two charged objects is directly proportional to the product 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 force between the charges,
k is the electrostatic constant (k = 9 × 10^9 N * m^2 / C^2),
|q1| and |q2| are the magnitudes of the charges, and
r is the distance between the charges.
Given that the negative charge is -2.0 μC (microcoulombs) and the positive charge is +3.0 μC (microcoulombs), we can substitute these values into the formula along with the distance of 8 cm (since we need to convert it to meters).
|q1| = 2.0 μC = 2.0 * 10^-6 C
|q2| = 3.0 μC = 3.0 * 10^-6 C
r = 8 cm = 8 * 10^-2 m
Now, we can calculate the force:
F = (9 × 10^9 N * m^2 / C^2) * ((2.0 * 10^-6 C) * (3.0 * 10^-6 C)) / (8 * 10^-2 m)^2
To simplify the calculation, we can first multiply the charges, then divide by the distance squared, and finally multiply by the electrostatic constant:
F = (9 × 10^9 N * m^2 / C^2) * (6.0 * 10^-12 C^2) / (6.4 * 10^-4 m^2)
Now, we can calculate the force by multiplying the electrostatic constant and the charge product, and then dividing by the square of the distance:
F = (9 × 10^9 N * m^2 / C^2) * (9.375 * 10^-8 N * m^2) / (6.4 * 10^-4 m^2)
F = 1.328 * 10^-2 N
Therefore, the force between the two charges is approximately 0.01328 N.