Three charges are arranged in a line. From left to right, the charges are:

Q1= -8mC, Q2 = +3mC and Q3 = -4mC. The distance between Q1 and Q2 is 0.3 m, and the distance between Q2 and Q3 is 0.2 m. Calculate the net electrostatic force on Q3.

Yes

-1.5 N

To calculate the net electrostatic force on Q3, we need to calculate the individual forces between Q3 and Q1, and Q3 and Q2, and then add them together.

The formula for 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
k is the electrostatic constant (k = 9 * 10^9 Nm^2/C^2)
Q1 and Q2 are the magnitudes of the charges
r is the distance between the charges

Let's calculate the force between Q3 and Q1 first.
Q1 = -8mC
Q3 = -4mC
The distance between Q1 and Q3 is 0.5 m (0.3 m + 0.2 m).

Substituting these values into Coulomb's Law:
F(3-1) = k * |Q1 * Q3| / r^2
F(3-1) = (9 * 10^9 Nm^2/C^2) * (8 * 10^-3 C) * (4 * 10^-3 C) / (0.5 m)^2

Simplifying the expression:
F(3-1) = (9 * 8 * 4 * 10^6 N * C^2) / (25 * 10^-2 m^2)
F(3-1) = 288 * 10^6 N * C^2 / 25 * 10^-2 m^2
F(3-1) = 288 * 10^6 N * C^2 / 2500 * 10^-2 m^2
F(3-1) = (288 / 2500) * 10^6 N * C^2 / m^2
F(3-1) = 0.1152 * 10^6 N * C^2 / m^2
F(3-1) = 115.2 * 10^3 N * C^2 / m^2
F(3-1) = 115.2 * 10^3 N * C^2 / m^2
F(3-1) = 115.2 * 10^3 N * C^2 / m^2

Therefore, the force between Q3 and Q1 is 115.2 * 10^3 N * C^2 / m^2.

Next, we calculate the force between Q3 and Q2.
Q2 = +3mC
Q3 = -4mC
The distance between Q2 and Q3 is 0.2 m.

Substituting these values into Coulomb's Law:
F(3-2) = k * |Q2 * Q3| / r^2
F(3-2) = (9 * 10^9 Nm^2/C^2) * (3 * 10^-3 C) * (4 * 10^-3 C) / (0.2 m)^2

Simplifying the expression:
F(3-2) = (9 * 3 * 4 * 10^6 N * C^2) / (4 * 10^-2 m^2)
F(3-2) = 108 * 10^6 N * C^2 / 4 * 10^-2 m^2
F(3-2) = 108 * 10^6 N * C^2 / 40 * 10^-2 m^2
F(3-2) = (108 / 40) * 10^6 N * C^2 / m^2
F(3-2) = 2.7 * 10^6 N * C^2 / m^2

Therefore, the force between Q3 and Q2 is 2.7 * 10^6 N * C^2 / m^2.

Now, to find the net electrostatic force on Q3, we add the forces together:

Net force on Q3 = F(3-1) + F(3-2)
Net force on Q3 = 115.2 * 10^3 N * C^2 / m^2 + 2.7 * 10^6 N * C^2 / m^2

Adding the forces:
Net force on Q3 = (115.2 * 10^3 N * C^2 + 2.7 * 10^6 N * C^2) / m^2
Net force on Q3 = 2.8152 * 10^6 N * C^2 / m^2

Therefore, the net electrostatic force on Q3 is 2.8152 * 10^6 N * C^2 / m^2.

Add the forces due to Q1 and Q2, upon Q3. They will be in opposite directions. Use Coulomb's law.

Note that the distance of Q1 from Q3 is 0.5 m

It will be a useful learning exercise, more so than having someone do it for you.