A charge of 3.93 is placed at each corner of a square 0.470 on a side.
Determine the magnitude of the force on each charge.
To determine the magnitude of the force on each charge, we can use Coulomb's Law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.
Here are the steps to calculate the magnitude of the force on each charge:
1. Determine the charge of each corner: In this case, each corner has a charge of 3.93.
2. Calculate the distance between the charges: Since the charges are placed at each corner of a square, and the side length of the square is given as 0.470, the distance between any two charges can be calculated using the Pythagorean theorem. In this case, the distance between any two charges will be the length of the diagonal of the square.
d = sqrt((0.470)^2 + (0.470)^2)
d = sqrt(0.2209 + 0.2209)
d = sqrt(0.4418)
d ≈ 0.664
3. Apply Coulomb's Law: Coulomb's Law states that the force (F) between two charges (q1 and q2) is given by the formula:
F = k * (|q1| * |q2|) / (d^2)
where k is the electrostatic constant (k ≈ 8.99 * 10^9 N·m^2/C^2), |q1| and |q2| are the magnitudes of the charges, and d is the distance between the charges.
4. Calculate the force on each charge: Since all four charges are the same (3.93), the force on each charge will be the same. We can calculate the force using the formula mentioned above:
F = (8.99 * 10^9) * (3.93 * 3.93) / (0.664^2)
F ≈ 2.87 * 10^11 N
So, the magnitude of the force on each charge is approximately 2.87 * 10^11 Newtons.