Let's solve this step by step.
### Given:
1. Charge 1 [tex]\( q_1 \)[/tex] = [tex]\( 2 \mu C \)[/tex] = [tex]\( 2 \times 10^{-6} \)[/tex] Coulombs
2. Charge 2 [tex]\( q_2 \)[/tex] = [tex]\( -2 nC \)[/tex] = [tex]\( -2 \times 10^{-9} \)[/tex] Coulombs
3. Distance [tex]\( r \)[/tex] between the charges = [tex]\( 0.1 mm \)[/tex] = [tex]\( 0.1 \times 10^{-3} \)[/tex] meters
### Step-by-Step Solution:
#### a) Magnitude of the Electric Force:
We will use Coulomb's Law to find the magnitude of the electric force between the charges. Coulomb's Law is given by:
[tex]\[ F = k \cdot \frac{|q_1 \cdot q_2|}{r^2} \][/tex]
Where:
- [tex]\( k \)[/tex] is Coulomb's constant, [tex]\( k \approx 8.99 \times 10^9 \, \frac{N \cdot m^2}{C^2} \)[/tex]
- [tex]\( q_1 \)[/tex] and [tex]\( q_2 \)[/tex] are the magnitudes of the charges
- [tex]\( r \)[/tex] is the distance between the charges
Now, let's substitute the values:
1. Calculate the product of the charges and take the absolute value:
[tex]\[ |q_1 \cdot q_2| = |(2 \times 10^{-6}) \cdot (-2 \times 10^{-9})| = 4 \times 10^{-15} \, C^2 \][/tex]
2. Calculate the square of the distance:
[tex]\[ r^2 = (0.1 \times 10^{-3})^2 = 0.1^2 \times 10^{-6} = 0.01 \times 10^{-6} = 10^{-8} \, m^2 \][/tex]
3. Substitute these values into Coulomb's Law:
[tex]\[ F = 8.99 \times 10^9 \cdot \frac{4 \times 10^{-15}}{10^{-8}} \][/tex]
4. Simplify the expression:
[tex]\[ F = 8.99 \times 10^9 \cdot 4 \times 10^{-7} \][/tex]
[tex]\[ F = 35.96 \times 10^2 \][/tex]
[tex]\[ F = 3596 \, N \][/tex]
So, the magnitude of the electric force between the charges is [tex]\( 3596 \, N \)[/tex].
#### b) Nature of the Force:
To determine whether the force is repulsive or attractive, we need to consider the signs of the charges involved:
- Charge 1 ([tex]\( q_1 \)[/tex]) = [tex]\( 2 \times 10^{-6} \)[/tex] Coulombs (positive)
- Charge 2 ([tex]\( q_2 \)[/tex]) = [tex]\( -2 \times 10^{-9} \)[/tex] Coulombs (negative)
When one charge is positive and the other is negative, the force between them is attractive.
Therefore, the force between the charges is attractive.
### Summary:
(a) The magnitude of the electric force between the charges is [tex]\( 3596 \, N \)[/tex].
(b) The force is attractive.
