The image shows a physics problem involving unit conversion and an equation with missing information. The equation involves the following:

$\left( -6.4 \times 10^5 \, \frac{\text{N}}{\text{C}^2 \cdot \text{m}^2} \right) \cdot \square = ? \, \frac{\text{N}}{\text{mC}^2 \cdot \text{m}^2}$

Where:

• $N$ stands for Newton (unit of force),
• $C$ stands for Coulomb (unit of electric charge),
• $m$ stands for meter (unit of distance),
• The missing part (represented by $\square$) is a factor needed to perform the conversion.

Step-by-step reasoning:

1. The left side involves $-6.4 \times 10^5 \, \frac{\text{N}}{\text{C}^2 \cdot \text{m}^2}$, while the right side involves $\frac{\text{N}}{\text{mC}^2 \cdot \text{m}^2}$. Notice the only difference between these two expressions is the unit of charge on the right side has been changed from $C^2$ to $\text{mC}^2$, where $\text{mC}$ stands for milliCoulomb.

2. $1 \, \text{C} = 1000 \, \text{mC}$, meaning: $1 \, \text{C}^2 = (1000 \, \text{mC})^2 = 10^6 \, \text{mC}^2$

3. To convert from $\frac{1}{C^2}$ to $\frac{1}{\text{mC}^2}$, we multiply by $10^6$, because $C^2$ is $10^6 \, \text{mC}^2$.

Conclusion:

The missing part of the equation should be $10^6$ to account for the conversion from Coulombs to milliCoulombs.

Would you like further details on this calculation? Here are five related questions:

1. How do we convert between other metric prefixes like kilo and micro?
2. What is the significance of Coulomb in physics, and why is this conversion important?
3. How does this equation relate to electrostatic force?
4. Could dimensional analysis be used to verify this type of unit conversion?
5. What would happen if the conversion factor was incorrect in practical scenarios?

Tip: Always double-check your unit conversions when dealing with different metric prefixes to avoid errors in calculations.