We are tasked with calculating the net electrostatic force on charge $A$ due to charges $B$ and $C$. Here’s how we can approach it:

Given Data:

• Charge $A = +3.0 \, \mu C$
• Charge $B = -1.5 \, \mu C$
• Charge $C = +4.0 \, \mu C$
• Distance between $A$ and $B = 0.20 \, \text{m}$
• Distance between $A$ and $C = 0.60 \, \text{m}$

Formula for Electrostatic Force:

The electrostatic force between two charges is given by Coulomb's Law: $F = k_e \cdot \frac{|q_1 \cdot q_2|}{r^2}$ where:

• $F$ is the magnitude of the force,
• $k_e = 8.99 \times 10^9 \, \text{N}\cdot\text{m}^2/\text{C}^2$ is Coulomb's constant,
• $q_1$ and $q_2$ are the magnitudes of the charges,
• $r$ is the distance between the charges.

Step-by-Step Calculation:

1. Force between $A$ and $B$:

• The force between $A$ and $B$ will be attractive (since $A$ is positive and $B$ is negative). $F_{AB} = k_e \cdot \frac{|(3.0 \times 10^{-6}) \cdot (-1.5 \times 10^{-6})|}{(0.20)^2}$ Let’s calculate $F_{AB}$.

2. Force between $A$ and $C$:

• The force between $A$ and $C$ will be repulsive (since both $A$ and $C$ are positive). $F_{AC} = k_e \cdot \frac{|(3.0 \times 10^{-6}) \cdot (4.0 \times 10^{-6})|}{(0.60)^2}$ Let’s calculate $F_{AC}$.

3. Determine the Net Force on $A$:

• The force between $A$ and $B$ is attractive (towards $B$) along the x-axis in the negative direction.
• The force between $A$ and $C$ is repulsive (away from $C$) along the x-axis in the positive direction.

Thus, the net force will be the algebraic sum: $F_{\text{net}} = F_{AC} - F_{AB}$ (Note: $F_{AC}$ will be positive and $F_{AB}$ will be negative because of direction.)

Let me calculate these values for you.The forces calculated are:

• Force between $A$ and $B$ (attractive): $F_{AB} = 1.011 \, \text{N}$ (acting towards $B$, negative direction).
• Force between $A$ and $C$ (repulsive): $F_{AC} = 0.300 \, \text{N}$ (acting away from $C$, positive direction).

Net Electrostatic Force on $A$:

$F_{\text{net}} = -0.712 \, \text{N}$ This means the net force on $A$ is $0.712 \, \text{N}$ towards charge $B$ (negative x-direction).

Would you like more details on how these values were calculated or need further clarifications?

Here are some related questions for practice:

1. How would the net force change if the sign of charge $C$ was negative?
2. What would happen to the net force if the distance between $A$ and $C$ doubled?
3. How would the net force on $A$ be affected if $B$ and $C$ had the same magnitude of charge?
4. What is the significance of the direction of the forces in Coulomb's law?
5. How does the medium (vacuum or other materials) between the charges affect the force?

Tip: In electrostatic problems, always consider both the magnitude and direction of forces to determine the net effect.