To determine the electrostatic force between two point charges, Coulomb's Law is employed. This law states that the force \( F \) is calculated using the equation:\[F = \frac{1}{4\pi\epsilon_0} \cdot \frac{|q_1 q_2|}{r^2},\]where: \( q_1 \) and \( q_2 \) represent the magnitudes of the charges, \( r \) is the separation distance between the charges, \( \frac{1}{4\pi\epsilon_0} = 9 \times 10^9 \, \mathrm{N \, m^2 \, C^{-2}} \) is Coulomb's constant.
Step 1: Input Values.Given values are:\[q_1 = 2 \, \mu \mathrm{C} = 2 \times 10^{-6} \, \mathrm{C}, \quad q_2 = -3 \, \mu \mathrm{C} = -3 \times 10^{-6} \, \mathrm{C}, \quad r = 10 \, \mathrm{cm} = 0.1 \, \mathrm{m}.\]Substituting these into Coulomb's Law yields:\[F = 9 \times 10^9 \cdot \frac{|(2 \times 10^{-6})(-3 \times 10^{-6})|}{(0.1)^2}.\]
Step 2: Calculation.Calculate the product of the charges:\[|q_1 q_2| = |(2 \times 10^{-6})(-3 \times 10^{-6})| = 6 \times 10^{-12}.\]Substitute this back into the formula:\[F = 9 \times 10^9 \cdot \frac{6 \times 10^{-12}}{0.01}.\]Simplify the expression:\[F = 9 \cdot 6 \cdot 10^{-3} = 54 \times 10^{-3} = 5.4 \, \mathrm{N}.\]
Step 3: Direction Determination.As \( q_1 \) and \( q_2 \) have opposite signs (\( + \) and \( - \)), the force between them is attractive.
Result:The magnitude of the force is \( 5.4 \, \mathrm{N} \), and the force is attractive.
Therefore, the correct answer is \( \mathbf{(1)} \).