A particle with charge −5 µC is located on
the x-axis at the point −4 cm , and a second
particle with charge −6 µC is placed on the
x-axis at 4 cm.
What is the magnitude of the total electrostatic
force on a third particle with charge
8 µC placed on the x-axis at 2 cm ? The
Coulomb constant is 8.9875 × 109 N · m2
/C
2
.
Answer in units of N
To find the magnitude of the total electrostatic force on the third particle, we can use the principle of superposition. This principle states that the total force on a charged particle due to multiple other charged particles is equal to the vector sum of the individual forces.
The formula to calculate the electrostatic force between two charged particles is given by Coulomb's Law:
F = (k * |q1 * q2|) / r^2
Where:
- F is the magnitude of the electrostatic force between the two charges,
- k is the Coulomb constant (8.9875 × 10^9 N·m^2/C^2),
- q1 and q2 are the charges of the particles, and
- r is the distance between the particles.
In this case, we have three charged particles:
- Particle 1 with charge q1 = -5 µC (-5 × 10^-6 C),
- Particle 2 with charge q2 = -6 µC (-6 × 10^-6 C), and
- Particle 3 with charge q3 = 8 µC (8 × 10^-6 C).
The distance between Particle 1 and Particle 3 is 6 cm (4 cm + 2 cm), and the distance between Particle 2 and Particle 3 is also 6 cm (4 cm - 2 cm).
To find the force between each pair of particles, we can substitute the values into Coulomb's Law:
Force between Particle 1 and Particle 3:
F1-3 = (k * |q1 * q3|) / r1-3^2
= (8.9875 × 10^9 N·m^2/C^2) * (|-5 × 10^-6 C * 8 × 10^-6 C|) / (0.06 m)^2
Force between Particle 2 and Particle 3:
F2-3 = (k * |q2 * q3|) / r2-3^2
= (8.9875 × 10^9 N·m^2/C^2) * (|-6 × 10^-6 C * 8 × 10^-6 C|) / (0.06 m)^2
To find the total force on Particle 3, we need to add the magnitudes of these forces:
Total force on Particle 3 = |F1-3| + |F2-3|
Now we can calculate the forces and find their sum:
F1-3 = (8.9875 × 10^9 N·m^2/C^2) * (40 × 10^-12 C^2) / (0.06 m)^2
≈ 1.498 N
F2-3 = (8.9875 × 10^9 N·m^2/C^2) * (48 × 10^-12 C^2) / (0.06 m)^2
≈ 1.798 N
Total force on Particle 3 = |1.498 N| + |1.798 N|
≈ 3.296 N
Therefore, the magnitude of the total electrostatic force on the third particle is approximately 3.296 N.