Four charges −8 × 10^−9 C at (0 m, 0 m),

−7 × 10^−9 C at (5 m, 1 m), −1 × 10^−9 C
at (−2 m, −3 m), and 2 × 10^−9 C at
(−2 m, 4 m), are arranged in the (x, y) plane as shown.

Find the magnitude of the resulting force on the -8c charge at the origin. The Coulomb constant is 8.98755 x 10^9.

Please help!

Freds answers are correct

To find the magnitude of the resulting force on the -8C charge at the origin, we need to calculate the individual forces created by each charge and then sum them up to get the net force.

The force between two charges can be calculated using Coulomb's law:

F = k * (|q1| * |q2|) / r^2

Where:
- F is the force between the charges
- k is the Coulomb constant (8.98755 x 10^9 N m^2/C^2)
- |q1| and |q2| are the magnitudes of the charges
- r is the distance between the charges.

Let's calculate the force created by each charge on the -8C charge at the origin:

1. Charge of -7 × 10^−9 C at (5 m, 1 m):
- Distance (r) = sqrt((5m - 0m)^2 + (1m - 0m)^2) = sqrt(25m^2 + 1m^2) = sqrt(26m^2)
- Force (F1) = (8.98755 x 10^9 N m^2/C^2) * (|-7 × 10^−9 C| * |8 × 10^−9 C|) / (sqrt(26m^2))^2

2. Charge of -1 × 10^−9 C at (−2 m, −3 m):
- Distance (r) = sqrt((-2m - 0m)^2 + (-3m - 0m)^2) = sqrt(4m^2 + 9m^2) = sqrt(13m^2)
- Force (F2) = (8.98755 x 10^9 N m^2/C^2) * (|-1 × 10^−9 C| * |8 × 10^−9 C|) / (sqrt(13m^2))^2

3. Charge of 2 × 10^−9 C at (−2 m, 4 m):
- Distance (r) = sqrt((-2m - 0m)^2 + (4m - 0m)^2) = sqrt(4m^2 + 16m^2) = sqrt(20m^2)
- Force (F3) = (8.98755 x 10^9 N m^2/C^2) * (|2 × 10^−9 C| * |8 × 10^−9 C|) / (sqrt(20m^2))^2

Now, we need to calculate the net force by summing up the individual forces:

Net force = F1 + F2 + F3

Using the given values and performing the calculations, you will obtain the magnitude of the resulting force on the -8C charge at the origin.