Using Coulomb's law, the electromagnetic force between two negatively charged particles, separated by 0.05 m with charges of -1.87 × 10^(-9) C and -1.10 × 10^(-9) C, is calculated to be 3.70 × 10^(-7) N.
To calculate the electromagnetic force between two charged particles, we use Coulomb's law, which is expressed by the formula:
F = k * |q1 * q2| / r^2
Where F is the force between the charges, k is Coulomb's constant (8.9875 × 10^9 N·m^2/C^2), q1 and q2 are the charges of the particles, and r is the distance between them.
Given that the charges are -1.87 × 10^(-9) C and -1.10 × 10^(-9) C and the distance between them is 0.05 m, we plug these values into Coulomb's law:
F = (8.9875 × 10^9 ) * |-1.87 × 10^(-9) * -1.10 × 10^(-9)| / (0.05)^2
After solving, the electromagnetic force comes out to be -3.70 × 10^(-7) N. The negative sign indicates that the force is attractive, which makes sense since both particles have negative charges. However, when reporting the magnitude of force, we often drop the sign, leading us to answer choice (D) 3.70 × 10^(-7) N.