There are three charges along the x axis Charge A = q1, Charge B = -q1, charge C = q2. q1 is positive 1.0 nC and is on the right, -q1 is in the middle with a 1cm distance between q1 and -q1, and q2 is on the right with 1cm distance to -q1 with a charge of 5.2 nC. What is the magnitude of the net electric force on charge A in newtons

To find the magnitude of the net electric force on charge A due to the other charges, we'll use Coulomb's law. The law states that the magnitude of the force between two point charges is given by:

\[
F = k \cdot \frac{|q_1 \cdot q_2|}{r^2}
\]

where:
- \( F \) is the magnitude of the force between the charges,
- \( k \) is Coulomb's constant \((8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2)\),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the distance between the charges.

### Given:
- \( q_1 = 1.0 \, \text{nC} = 1.0 \times 10^{-9} \, \text{C} \) (Charge A)
- \( -q_1 = -1.0 \, \text{nC} = -1.0 \times 10^{-9} \, \text{C} \) (Charge B)
- \( q_2 = 5.2 \, \text{nC} = 5.2 \times 10^{-9} \, \text{C} \) (Charge C)
- Distance between Charge A and Charge B = 1 cm = \(0.01 \, \text{m}\)
- Distance between Charge A and Charge C = 2 cm = \(0.02 \, \text{m}\)

### Step 1: Calculate the force on Charge A due to Charge B
\[
F_{AB} = k \cdot \frac{|q_1 \cdot (-q_1)|}{(0.01)^2}
\]

\[
F_{AB} = (8.99 \times 10^9) \cdot \frac{(1.0 \times 10^{-9}) \cdot (1.0 \times 10^{-9})}{0.01^2}
\]

\[
F_{AB} = (8.99 \times 10^9) \cdot \frac{1.0 \times 10^{-18}}{1.0 \times 10^{-4}}
\]

\[
F_{AB} = (8.99 \times 10^9) \cdot 1.0 \times 10^{-14} = 8.99 \times 10^{-5} \, \text{N}
\]

This force is attractive, so it acts to the left (toward Charge B).

### Step 2: Calculate the force on Charge A due to Charge C
\[
F_{AC} = k \cdot \frac{|q_1 \cdot q_2|}{(0.02)^2}
\]

\[
F_{AC} = (8.99 \times 10^9) \cdot \frac{(1.0 \times 10^{-9}) \cdot (5.2 \times 10^{-9})}{0.02^2}
\]

\[
F_{AC} = (8.99 \times 10^9) \cdot \frac{5.2 \times 10^{-18}}{4.0 \times 10^{-4}}
\]

\[
F_{AC} = (8.99 \times 10^9) \cdot 1.3 \times 10^{-14} = 1.1697 \times 10^{-4} \, \text{N}
\]

This force is repulsive, so it acts to the right (away from Charge C).

### Step 3: Calculate the net force on Charge A
Since \( F_{AB} \) acts to the left and \( F_{AC} \) acts to the right, the net force \( F_{\text{net}} \) on Charge A is:

\[
F_{\text{net}} = F_{AC} - F_{AB}
\]

\[
F_{\text{net}} = 1.1697 \times 10^{-4} \, \text{N} - 8.99 \times 10^{-5} \, \text{N}
\]

\[
F_{\text{net}} = 2.7 \times 10^{-5} \, \text{N}
\]

### Final Answer:
The magnitude of the net electric force on charge A is approximately \( 2.7 \times 10^{-5} \, \text{N} \), directed to the right.

Would you like more details or have any questions?

---

1. How would the result change if the distance between the charges were doubled?
2. What would happen to the net force if \( q_2 \) were a negative charge instead of positive?
3. Can you find the force on Charge B due to the other charges?
4. What would the net force on Charge A be if all charges were the same magnitude?
5. How does the direction of the forces change if Charge A is negative?

**Tip:** Always double-check the distances used in Coulomb's law calculations, as they are squared in the formula, making them crucial to accurate results.

There are three charges along the x-axis: Charge A = q1, Charge B = -q1, charge C = q2. q1 is positive 1.0 nC and is on the left, -q1 is in the middle with a 1 cm distance between q1 and -q1, and q2 is on the right with a 1 cm distance to -q1 with a charge of 5.2 nC. What is the magnitude of the net electric force on charge A in newtons?

Find out how to calculate the net electric force on a charge along the x-axis using Coulomb's law. This example problem includes detailed calculations of forces due to multiple charges and is suitable for undergraduate physics students.

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