Three charges are arranged as follows: +3 mC located on the y-axis at +15 mm; -2.5 mC located on the x-axis at -25 mm; and +4.0 mC located at the origin. Determine the magnitude of the force acting on the charge located at the origin.

Use coulombs law, add the forces as vectors. You have a S force from the y charge, and a W force from the x axis charge.

To determine the magnitude of the force acting on the charge located at the origin, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is proportional to the product of the charges and inversely proportional to the square of the distance between them.

Let's compute the forces between the charge at the origin and the other two charges separately, and then add them vectorially.

Step 1: Calculate the force between the charge at the origin (+4.0 mC) and the charge on the y-axis (+3 mC).

Given:
Charge 1 (q1) = +4.0 mC = 4.0 × 10^(-3) C
Charge 2 (q2) = +3.0 mC = 3.0 × 10^(-3) C
Distance (r) = 15 mm = 15 × 10^(-3) m

Using Coulomb's Law formula:
F = (k * |q1 * q2|) / r^2
where k is Coulomb's constant = 9 × 10^9 Nm^2/C^2

F1 = (9 × 10^9 Nm^2/C^2 * |(4.0 × 10^(-3) C) * (3.0 × 10^(-3) C)|) / (15 × 10^(-3) m)^2

F1 = (9 × 10^9 Nm^2/C^2 * (4.0 × 10^(-3) C) * (3.0 × 10^(-3) C)) / (15 × 10^(-3) m)^2

F1 ≈ 3800 N

Step 2: Calculate the force between the charge at the origin (+4.0 mC) and the charge on the x-axis (-2.5 mC).

Given:
Charge 1 (q1) = +4.0 mC = 4.0 × 10^(-3) C
Charge 2 (q2) = -2.5 mC = -2.5 × 10^(-3) C
Distance (r) = 25 mm = 25 × 10^(-3) m

Using Coulomb's Law formula:
F = (k * |q1 * q2|) / r^2

F2 = (9 × 10^9 Nm^2/C^2 * |(4.0 × 10^(-3) C) * (-2.5 × 10^(-3) C)|) / (25 × 10^(-3) m)^2

F2 = (9 × 10^9 Nm^2/C^2 * (4.0 × 10^(-3) C) * (-2.5 × 10^(-3) C)) / (25 × 10^(-3) m)^2

F2 ≈ -720 N

Step 3: Add the forces vectorially to find the total force on the charge located at the origin.

Total Force = F1 + F2 = 3800 N + (-720 N)

Total Force ≈ 3080 N

Therefore, the magnitude of the force acting on the charge located at the origin is approximately 3080 N.

To determine the magnitude of the force acting on the charge located at the origin, we can use Coulomb's law, which states that the force between two charges is given by the equation:

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

Where:
- F is the force between the charges,
- k is the electrostatic constant, approximately equal to 8.99 x 10^9 N m^2/C^2,
- q1 and q2 are the magnitudes of the charges, and
- r is the distance between the charges.

In this case, we have three charges: +3 mC, -2.5 mC, and +4.0 mC. Let's consider the force acting on the charge located at the origin, which is +4.0 mC.

First, we need to calculate the distances between the charges. From the given information, we know that the +3 mC charge is located on the y-axis at +15 mm, the -2.5 mC charge is located on the x-axis at -25 mm, and the +4.0 mC charge is at the origin (0,0).

To calculate the distances between the charges, we use the Pythagorean theorem:

For the +3 mC charge:
Distance = sqrt((0 - 0)^2 + (0 - 15)^2) = sqrt(0 + 225) = sqrt(225) = 15 mm.

For the -2.5 mC charge:
Distance = sqrt((0 - (-25))^2 + (0 - 0)^2) = sqrt(625 + 0) = sqrt(625) = 25 mm.

Now, we can calculate the magnitude of the force acting on the charge at the origin using Coulomb's law:

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

F = (8.99 x 10^9 N m^2/C^2) * ((4.0 x 10^-3 C) * (3.0 x 10^-3 C)) / (15 x 10^-3 m)^2

F = (8.99 x 10^9 N m^2/C^2) * (12.0 x 10^-6 C^2) / (225 x 10^-6 m^2)

F = (8.99 x 12.0 x 10^3 N) / (225)

F = 539.28 N

Therefore, the magnitude of the force acting on the charge located at the origin is approximately 539.28 N.