Final answer:
The value of each of the equal charges that repel each other with a force of 0.1 N when situated 50 cm apart in a vacuum is approximately 1.7 μC. Hence, option (a) is correct.
Step-by-step explanation:
To calculate the value of two equal charges that repel each other with a known force, we utilize Coulomb's law, which is represented by the following equation:
F = k \cdot \fracq1 \cdot q2{r^2}
Where:
- F is the electrostatic force between the charges (in newtons)
- k is Coulomb's constant (8.9875 \times 10^9 N m^2/C^2)
- q1 and q2 are the magnitudes of the two charges (in coulombs)
- r is the distance between the charges (in meters)
Given that the two charges are equal, we can say q1 = q2 = q.
Plugging in the known values:
0.1 N = (8.9875 \times 10^9 N m^2/C^2) \cdot \frac{q^2}{(0.50 m)^2}
Now we solve for q:
q^2 = \frac{0.1 N \cdot (0.50 m)^2}{8.9875 \times 10^9 N m^2/C^2}
q^2 = \frac{0.025 N m^2}{8.9875 \times 10^9 N m^2/C^2}
q^2 = 2.78 \times 10^{-12} C^2
q = \sqrt{2.78 \times 10^{-12} C^2}
q = 1.67 \times 10^{-6} C
q = 1.67 μC
Hence, the value of each charge is approximately 1.7 μC, which corresponds to option (a).