Two point charges are fixed on the y axis: a negative point charge q1 = -26 µC at y1 = +0.21 m and a positive point charge q2 at y2 = +0.38 m. A third point charge q = +8.5 µC is fixed at the origin. The net electrostatic force exerted on the charge q by the other two charges has a magnitude of 24 N and points in the +y direction. Determine the magnitude of q2.

To determine the magnitude of q2, we need to use Coulomb's Law and set up an equation based on the given information.

Coulomb's Law states that the electrostatic force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, it can be expressed as:

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

where F is the electrostatic force, k is the Coulomb's constant (9 x 10^9 Nm^2/C^2), |q1| and |q2| are the magnitudes of the charges, and r is the distance between the charges.

We are given that the net electrostatic force exerted on charge q is 24 N and points in the +y direction. This means that the forces exerted by both q1 and q2 on q must be equal in magnitude and opposite in direction. Therefore, we can set up the equation:

24 N = k * |q1| * |q| / r1^2

Since q1 is a negative charge, we need to take its magnitude (26 µC) into account. We are also given that q = +8.5 µC.

The distance between q and q1 is given by the y-coordinate difference between their positions:

r1 = |y2 - y1| = |0.38 m - 0.21 m| = 0.17 m

Now, we can substitute the values into the equation to solve for q2:

24 N = (9 x 10^9 Nm^2/C^2) * (26 µC) * (8.5 µC) / (0.17 m)^2

Solving this equation will give us the magnitude of q2.