Exam Question:

A positive point charge with a magnitude of 2 μC is placed at the origin of an x-y coordinate system. Another positive point charge with a magnitude of 4 μC is placed on the x-axis at a distance of 3 meters from the origin. Determine the electric force exerted on the 2 μC charge due to the 4 μC charge.

Answer:

To determine the electric force between the two charges, we can use Coulomb's Law. Coulomb's Law states that the electric force between two point charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. Mathematically, it can be represented as:

Where:

• F is the electric force between the charges,
• k is the electrostatic constant, equal to $8.99 \times 10^9 \, \text{N} \cdot \text{m}^2/\text{C}^2$,
• $q_1$ and $q_2$ are the magnitudes of the two charges, and
• r is the distance between the charges.

Given that $q_1 = 2 \, \mu\text{C}$, $q_2 = 4 \, \mu\text{C}$, and $r = 3 \, \text{m}$, we can substitute these values into Coulomb's Law and find the electric force.

Simplifying the expression:

Therefore, the electric force exerted on the 2 μC charge due to the 4 μC charge is approximately 7.99 mN (millinewtons).