To calculate the magnitude of the electric force acting on the negatively charged particle $Q_2$, we can use Coulomb's Law, which describes the force between two point charges:

$F = \frac{{k_e |Q_1 Q_2|}}{{r^2}}$

Where:

• $F$ is the magnitude of the electric force.
• $k_e$ is Coulomb's constant, which is approximately $8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$.
• $Q_1$ and $Q_2$ are the charges.
• $r$ is the distance between the charges.

Given values:

• $Q_1 = 35 \, \text{nC} = 35 \times 10^{-9} \, \text{C}$
• $Q_2 = -8 \, \text{nC} = -8 \times 10^{-9} \, \text{C}$
• $r = d = 25 \, \text{cm} = 0.25 \, \text{m}$

Substituting these values into Coulomb's Law:

$F = \frac{{(8.99 \times 10^9) \times |(35 \times 10^{-9}) \times (-8 \times 10^{-9})|}}{{(0.25)^2}}$

First, calculate the product of the charges $|Q_1 Q_2|$:

$|Q_1 Q_2| = |(35 \times 10^{-9}) \times (-8 \times 10^{-9})| = 280 \times 10^{-18} \, \text{C}^2$

Now substitute into the equation:

$F = \frac{{8.99 \times 10^9 \times 280 \times 10^{-18}}}{{(0.25)^2}}$

Now let's calculate the value:

$F = \frac{{8.99 \times 10^9 \times 280 \times 10^{-18}}}{{0.0625}} = \frac{{2.5172 \times 10^{-7}}}{{0.0625}} = 4.03 \times 10^{-6} \, \text{N}$

Final answer:

The magnitude of the electric force acting on $Q_2$ is:

$F = 4.03 \, \mu\text{N}$

Would you like to go over any details, or do you have additional questions?

Here are some related questions:

1. How does the direction of the force on $Q_2$ depend on the signs of the charges?
2. How does Coulomb's law change when the charges are in a vacuum versus another medium?
3. What is the effect of increasing the distance between the two charges on the force?
4. How would the force change if the charge $Q_2$ were moved to the negative x-axis?
5. What is the relationship between the electric force and the gravitational force on a particle of this mass?

Tip: Remember that the magnitude of the force between two charges is inversely proportional to the square of the distance between them (this is the $r^2$ term in Coulomb's law).