A pair of charges exert attractive forces of magnitude 2.4*10^-2 N on each other when they are separated by 2.0 m. The total charge of the pair is +3.0 Micro Coulomb. What is the charge on the object with positive/negative charge?
To find the charge on the object with positive or negative charge in this pair, we can use Coulomb's law, which states that the force between two charges is directly proportional to the product of their 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 two charges,
k is the Coulomb's constant (8.99 x 10^9 N*m^2/C^2),
q1 and q2 are the magnitudes of the two charges, and
r is the distance between the charges.
In this case, we have the force (2.4 x 10^-2 N) and the distance (2.0 m). The total charge of the pair is given as +3.0 µC.
Let's calculate the charge on the object with positive/negative charge:
1. Convert the total charge from micro-Coulombs to Coulombs:
+3.0 µC = +3.0 x 10^-6 C
2. Rearrange the Coulomb's law formula to solve for the charge:
q1 = (F * r^2) / (k * q2)
3. Substitute the known values into the formula:
q1 = (2.4 x 10^-2 N * (2.0 m)^2) / (8.99 x 10^9 N*m^2/C^2 * +3.0 x 10^-6 C)
4. Calculate the charge on the object:
q1 ≈ +1.066 x 10^-8 C
Therefore, the charge on the object with positive/negative charge is approximately +1.066 x 10^-8 Coulombs.