A particle with charge 7 µC is located on the

x-axis at the point 4 cm , and a second particle
with charge 7 µC is placed on the x-axis at
6 cm .
−10−8 −6 −4 −2 2 4 6 8 10
7
µ
C
7
µ
C
8
µ
C
x → (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 with charge 8 µC, we can use the principle of superposition. This principle states that the net force on a charged particle due to multiple charged particles is the vector sum of the individual forces exerted by each charged particle.

The electrostatic force between two point charges can be calculated using Coulomb's law:

F = k * (q1 * q2) / r^2

Where F is the magnitude of the force, 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 them.

In this case, we have three particles:

Particle 1: Charge = 7 µC, located at 4 cm on the x-axis.
Particle 2: Charge = 7 µC, located at 6 cm on the x-axis.
Particle 3: Charge = 8 µC, located at 2 cm on the x-axis.

We need to calculate the forces between Particle 3 and Particle 1, and between Particle 3 and Particle 2. The forces will be attractive if the charges have opposite signs, and repulsive if the charges have the same signs.

Force between Particle 3 and Particle 1:
q1 = 8 µC, q2 = 7 µC, r = distance between them = |2 cm - 4 cm| = 2 cm
Calculate the force using Coulomb's law.

Force between Particle 3 and Particle 2:
q1 = 8 µC, q2 = 7 µC, r = distance between them = |2 cm - 6 cm| = 4 cm
Calculate the force using Coulomb's law.

Finally, find the vector sum of these two forces to obtain the net force on Particle 3. The magnitude of this net force will be the answer to the question, which is to be expressed in units of N (Newtons).