Consider 2 charged objects. One has a negative charge if 18 colombs. The 1 charges are separated by a distance if 0.9 m and a force of -2.7 N exists between them. Determine the charge of the other object.
The force between them, together with Coulomb's law, will tell you the value of the product Q1*Q2. Since you know Q1 = -18 already, you can solve for Q2.
It is not clear whether the - sign in front of the force indicates the charges attract or repel.
To determine the charge of the other object, we can use the formula for the electric force between two charged objects:
F = (k * Q1 * Q2) / r^2
Where:
F is the force between the two objects
k is the electrostatic constant (k ≈ 9 × 10^9 N m^2/C^2)
Q1 and Q2 are the charges of the two objects
r is the distance between the two objects
In this case, we have the force (F) as -2.7 N, the charge of one object (Q1) as -18 C, and the distance (r) as 0.9 m. We need to solve for the charge of the other object (Q2).
Rearranging the formula, we get:
Q2 = (F * r^2) / (k * Q1)
Substituting the given values into the equation:
Q2 = (-2.7 N * (0.9 m)^2) / (9 × 10^9 N m^2/C^2 * -18 C)
Simplifying:
Q2 = (-2.43 N*m^2) / (-1.62 × 10^11 N m^2/C)
Cancelling units:
Q2 = 1.5 × 10^-11 C
Therefore, the charge of the other object is approximately 1.5 × 10^-11 Coulombs.