Chapter 18, Problem 13
Two point charges are fixed on the y axis: a negative point charge q1 = -26 μC at y1 = +0.17 m and a positive point charge q2 at y2 = +0.35 m. A third point charge q = +9.5 μC is fixed at the origin. The net electrostatic force exerted on the charge q by the other two charges has a magnitude of 26 N and points in the +y direction. Determine the magnitude of q2.
To find the magnitude of q2, we need to use Coulomb's Law. Coulomb's Law states that the electrostatic force between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between them.
The formula for Coulomb's Law is:
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 magnitudes of the charges
- r is the distance between the charges
In this problem, we have two charges q1 and q2 exerting a net electrostatic force on charge q. We are given all the other variables in the problem, including the magnitude and direction of the net force.
Let's break down the problem step by step:
Step 1: Calculate the distance between q and q1
- The distance between q and q1 is the y-coordinate of q1 (y1 = +0.17 m)
Step 2: Calculate the distance between q and q2
- The distance between q and q2 is the y-coordinate of q2 (y2 = +0.35 m)
Step 3: Calculate the magnitude of q1's force on q
- We are given that the net force exerted on q by q1 and q2 has a magnitude of 26 N and points in the +y direction.
- Since the net force is in the +y direction, it means the force due to q1 must also be in the +y direction.
Step 4: Use Coulomb's Law to find the magnitude of q2
- Rearrange the Coulomb's Law equation to solve for |q2|:
|q2| = (F * r^2) / (k * |q1|)
- Plug in the known values for F, r, k, and |q1| to find |q2|.
By following these steps, we can calculate the magnitude of q2 and find the answer to the problem.