Final answer:
The magnitude of the force on the positive 5uC charge at the midpoint between two point charges of 9uC and 4uC placed 4m apart is 20.25 Newtons.
Step-by-step explanation:
To calculate the magnitude of the force on a positive 5uC charge at the midpoint between two point charges of 9uC and 4uC placed 4m apart, we can use Coulomb's Law. Coulomb's Law states that the magnitude of the electrostatic force between two point charges 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) / r²
Where:
- F is the magnitude of the force
- k is the electrostatic constant
- q1 and q2 are the charges of the point charges
- r is the distance between the point charges
Plugging in the values:
- q1 = 9uC
- q2 = 4uC
- r = 4m
- k = 9 x 10⁹ Nm²/C² (electrostatic constant)
we can calculate the force:
F = (9 x 10⁹ Nm²/C²) * ((9uC * 4uC) / (4m)²)
Simplifying the calculation:
F = (9 x 10⁹) * (36uC²) / 16m²
F = 20.25N
The magnitude of the force on the positive 5uC charge at the midpoint is 20.25 Newtons.