Short Answer 
The process to find the charges qA and qB begins with the formula qA * qB = k * F * r², using given values for k, F, and r to calculate qA * qB = 1.5 x 10^-16 C². Then, substituting the relationship qB = 25 nC РqA into the quadratic equation allows for solving qA, yielding two possible values: 10 nC and 15 nC for qA, with qB being the corresponding value from 25 nC.
Step 1: Understand the Formula
To begin solving for the charges qA and qB, we first need to understand the fundamental formula used in this scenario. The formula guiding us is:
- qA * qB = k * F * r²
In this formula, k represents Coulomb’s constant, F is the force, and r is the distance between the charges. We’ll substitute the values for F, r, and k to proceed with calculations.
Step 2: Substitute Values
Next, we will substitute the known values into the equation. Here, we apply the given values:
- k = 9.0 x 10^9 N·m²/C²,
- F = 5.4 x 10^-4 N,
- r = 0.050 m.
By plugging these into our earlier formula, we find:
- qA * qB = (9.0 x 10^9) * (5.4 x 10^-4) * (0.050)²
This calculation results in qA * qB = 1.5 x 10^-16 C².
Step 3: Solve the Quadratic Equation
Finally, we need to solve for qA using the quadratic equation. The relationship between qB and qA is given as:
- qB = 25 nC – qA.
Substituting this into the equation qA * (25 nC РqA) = 1.5 x 10^-16 C² gives us:
- This forms a quadratic equation that can be solved resulting in qA = 10 nC or qA = 15 nC.
- Accordingly, qB will be the remaining value from 25 nC.