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 = +0.30 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 25 N and points in the +y direction. Determine the magnitude of q2.

Question

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 = +0.30 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 25 N and points in the +y direction. Determine the magnitude of q2.

Answer 1

To determine the magnitude of q2, we can use Coulomb's Law, which states that the magnitude of 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.

Let's break down the problem step by step:

Step 1: Calculate the distance between q and q1.
The distance between two points in one dimension is simply the absolute difference between their y-coordinates.
d1 = |y - y1| = |0.30 m - 0.21 m| = 0.09 m

Step 2: Calculate the distance between q and q2.
Since q2 is at the origin, the distance between q and q2 is simply the y-coordinate of q.
d2 = y = 0.30 m

Step 3: Use Coulomb's Law to find the force between q and q1.
F1 = k * |q * q1| / d1^2

Step 4: Use Coulomb's Law to find the force between q and q2.
F2 = k * |q * q2| / d2^2

Step 5: Find the net force.
Since the net electrostatic force exerted on q by the other two charges points in the +y direction, it means that the forces F1 and F2 must have opposite directions.
Thus, we can write:
Net force = F1 - F2 = 25 N

Step 6: Substitute the force equations into the net force equation and solve for q2.
F1 - F2 = k * |q * q1| / d1^2 - k * |q * q2| / d2^2 = 25 N

Now, we can rearrange the equation to solve for q2:
k * |q * q2| / d2^2 = k * |q * q1| / d1^2 - 25 N

Since k and q are constants, we can cancel them on both sides of the equation:
|q2| / d2^2 = |q1| / d1^2 - 25 N

Now, substitute the given values:
|q2| / (0.30 m)^2 = (26 µC) / (0.09 m)^2 - 25 N

Rearrange the equation to solve for |q2|:
|q2| = [(26 µC) / (0.09 m)^2 - 25 N] * (0.30 m)^2

Calculating the right-hand side of the equation will give us the magnitude of q2. Remember to convert µC to C before performing the calculations.

Please note that the constant k in Coulomb's Law is 8.99 x 10^9 N m^2/C^2.