1. What is (a)the magnitude of the electrostatic force on a 10 microCoulomb charge located at the origin due to a 3 microCoulomb charge located at 1,-2? (b) What is the force on the 3 microCoulomb charge? Write your answer in component notation.

To find the magnitude of the electrostatic force between two charges, we can use Coulomb's Law given by the equation:

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

Where:
- F is the magnitude of the electrostatic force
- k is the electrostatic constant (8.99 x 10^9 Nm^2/C^2)
- |q1| and |q2| are the magnitudes of the charges
- r is the distance between the charges

(a) To find the magnitude of the electrostatic force on a 10 microCoulomb charge located at the origin (0, 0) due to a 3 microCoulomb charge located at (1, -2), we need to determine the distance between the charges.
The distance between two points (x1, y1) and (x2, y2) can be calculated using the distance formula:

r = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the values, we have:

r = sqrt((1 - 0)^2 + (-2 - 0)^2)
= sqrt(1^2 + (-2)^2)
= sqrt(1 + 4)
= sqrt(5)

Now we can calculate the magnitude of the electrostatic force F:

F = (8.99 x 10^9 Nm^2/C^2) * ((10 x 10^-6 C) * (3 x 10^-6 C)) / (sqrt(5))^2
= (8.99 x 10^9 Nm^2/C^2) * (30 x 10^-12 C^2) / 5
= (8.99 x 10^9 Nm^2/C^2) * (6 x 10^-12 C^2)
= 53.94 N

Therefore, the magnitude of the electrostatic force on the 10 microCoulomb charge is 53.94 Newtons.

(b) To find the force on the 3 microCoulomb charge, we can use the same magnitude but with opposite direction as per Newton's third law. So the force on the 3 microCoulomb charge will be -53.94 Newtons.

In component notation, the force on the 3 microCoulomb charge can be written as:

Fx = -53.94 N
Fy = 0 N

So, the force on the 3 microCoulomb charge is given by (-53.94 N, 0 N) in component notation.