1) Particles of charge Q1 = +77 µC, Q2 = +44 µC, and Q3 = -80 µC are placed in a line. The center one (Q2) is 0.35 m from each of the others. Calculate the net force on Q1 and Q2 due to the other charges.

a) Force on Q1
Magnitude

b) Force on Q2
Magnitude

2) A charge of 3.9 nC and a charge of 5.9 nC are separated by 7 m. Find the equilibrium position for a -4.2 nC charge.

the chargd 3.9 nc and the charge 5.7 separated by 7m

To calculate the net force on each charge, we can use Coulomb's Law. Coulomb's Law states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them.

1) Force on Q1:

First, we need to calculate the distances between Q1 and Q2 as well as between Q1 and Q3.
Given:
Q1 = +77 µC = +77 × 10^(-6) C
Q2 = +44 µC = +44 × 10^(-6) C
Q3 = -80 µC = -80 × 10^(-6) C
Distance between Q1 and Q2 = 0.35 m
Distance between Q1 and Q3 = 0.35 m

Using Coulomb's Law:
Force on Q1 due to Q2:
F1-2 = (k × |Q1 × Q2|) / (r^2)
where k is the electrostatic constant and is equal to 8.99 × 10^9 N·m^2/C^2, and r is the distance between Q1 and Q2 in meters.

Let's calculate the force on Q1 due to Q2:
F1-2 = (8.99 × 10^9 N·m^2/C^2) × (|+77 × 10^(-6) C × +44 × 10^(-6) C|) / (0.35 m)^2

Simplifying this expression gives us the magnitude of the force on Q1 due to Q2.

2) Force on Q2:

Similarly, we can calculate the force on Q2 due to Q1 and Q3.
Force on Q2 due to Q1:
F2-1 = (k × |Q2 × Q1|) / (r^2)

Force on Q2 due to Q3:
F2-3 = (k × |Q2 × Q3|) / (r^2)

By calculating these two forces using Coulomb's Law, you can find the net force on Q2.

2) Equilibrium position for a charge of -4.2 nC when separated by charges of 3.9 nC and 5.9 nC:

To find the equilibrium position for the -4.2 nC charge, we need to consider the forces between all three charges. In equilibrium, the net force on the -4.2 nC charge should be zero.

Using Coulomb's Law, we can calculate the forces between the charges:

Force on -4.2 nC due to 3.9 nC:
F-4.2-3.9 = (k × |-4.2 × 10^(-9) C × 3.9 × 10^(-9) C|) / (7 m)^2

Force on -4.2 nC due to 5.9 nC:
F-4.2-5.9 = (k × |-4.2 × 10^(-9) C × 5.9 × 10^(-9) C|) / (7 m)^2

To find the equilibrium position, we need to set the net force on the -4.2 nC charge equal to zero and solve for the distance between the charges.

F-4.2-3.9 + F-4.2-5.9 = 0

By rearranging the equation and solving for the distance, you can determine the equilibrium position for the -4.2 nC charge.

To calculate the net force on Q1 and Q2, we can use Coulomb's Law, which states that the force between two charges is given by:

F = k * |Q1 * Q2| / r^2

where F is the force, k is the electrostatic constant (8.99 x 10^9 N * m^2 / C^2), Q1 and Q2 are the charges, and r is the distance between them.

Let's calculate the forces step by step:

1) Force on Q1:
Q1 = +77 µC = 77 x 10^-6 C
Q2 = +44 µC = 44 x 10^-6 C
Q3 = -80 µC = -80 x 10^-6 C
r = 0.35 m

Using Coulomb's Law, the magnitude of the force on Q1 due to Q2 is:
F12 = k * |Q1 * Q2| / r^2
F12 = (8.99 x 10^9 N * m^2 / C^2) * |(77 x 10^-6 C) * (44 x 10^-6 C)| / (0.35 m)^2

Calculating this expression gives us the magnitude of the force on Q1.

2) Force on Q2:
Using Coulomb's Law, the magnitude of the force on Q2 due to Q1 is:
F21 = k * |Q1 * Q2| / r^2
F21 = (8.99 x 10^9 N * m^2 / C^2) * |(77 x 10^-6 C) * (44 x 10^-6 C)| / (0.35 m)^2

Calculating this expression gives us the magnitude of the force on Q2.

Now, let's move on to the next question:

3) Equilibrium position for a -4.2 nC charge:
Charge 1 (3.9 nC) is positive, and charge 2 (5.9 nC) is also positive. The equilibrium position for the -4.2 nC charge lies between the two positive charges, where the net electrostatic force exerted on the negative charge is zero.

Since the 2 positive charges are separated by 7 m, the negative charge should be placed at a distance x from the 3.9 nC charge and at a distance of 7 - x from the 5.9 nC charge.

Using Coulomb's Law, the magnitude of the force on the -4.2 nC charge due to the 3.9 nC charge is:
F1 = k * |Q1 * Q2| / r^2
F1 = (8.99 x 10^9 N * m^2 / C^2) * |(-4.2 x 10^-9 C) * (3.9 x 10^-9 C)| / (x m)^2

Similarly, the magnitude of the force on the -4.2 nC charge due to the 5.9 nC charge is:
F2 = k * |Q1 * Q2| / r^2
F2 = (8.99 x 10^9 N * m^2 / C^2) * |(-4.2 x 10^-9 C) * (5.9 x 10^-9 C)| / ((7 - x) m)^2

To find the equilibrium position, we need to set the sum of the forces F1 and F2 equal to zero and solve for x. Once we find the value of x, we can determine the equilibrium position.