A particle of charge +1.00 x 10e-6 C is 15.0 cm distant from a second particle of charge -3.00 x 10e-6 C. Calculate the magnitude of the electrostatic force between the particles.

Learn and apply Coulomb's law.

F = k Q1*Q2/R^2

That will give you the magnitude of the force,
The direction of the force will be towards the other particle, since they have opposite signs.

Is your e-6 supposed to represent 10^-6? The latter would be a better way to write it. e-6 is easily confused with e^-6. E-6 is computer jargon.

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To calculate the magnitude of the electrostatic force between two charged particles, you can use Coulomb's Law. Coulomb's Law states that the magnitude of the electrostatic force (F) between two charged particles is directly proportional to the product of their charges (q1 and q2) and inversely proportional to the square of the distance (r) between them. Mathematically, it can be written as:

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

Where:
F is the magnitude of the electrostatic force,
k is the electrostatic constant (k = 8.99 x 10^9 N m^2/C^2),
q1 and q2 are the charges of the particles,
|r| is the absolute value of the distance between the particles.

In this case, you have a particle with a charge of +1.00 x 10^-6 C and a second particle with a charge of -3.00 x 10^-6 C. The distance between them is 15.0 cm (or 0.15 m).

Let's substitute the values into Coulomb's Law and calculate the magnitude of the electrostatic force:

F = (8.99 x 10^9 N m^2/C^2) * [(+1.00 x 10^-6 C) * (-3.00 x 10^-6 C)] / (0.15 m)^2

F = (8.99 x 10^9 N m^2/C^2) * (-3.00 x 10^-12 C^2) / (0.0225 m^2)

F = -8.99 x 3.00 x 10^-3 N

F = -26.97 x 10^-3 N

Taking the magnitude of the force (ignoring the negative sign due to its direction), we get:

|F| = 26.97 x 10^-3 N

So, the magnitude of the electrostatic force between the two particles is approximately 26.97 x 10^-3 N.