The force between two identical charges seperated by 0.01m is equal to 95N. What is the magnitude of the two charges?

To determine the magnitude of the two identical charges, we can use Coulomb's Law, which states:

\[ F = k_e \frac{q_1 q_2}{r^2} \]

where:
- \( F \) is the force between the charges,
- \( k_e \) is Coulomb's constant (\(8.9875 \times 10^9 \, \text{Nm}^2/\text{C}^2\)),
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges,
- \( r \) is the separation between the charges.

Given:
- \( F = 95 \, \text{N} \),
- \( r = 0.01 \, \text{m} \),
- \( q_1 = q_2 = q \).

Substituting the given values into Coulomb's Law, we get:

\[ 95 = 8.9875 \times 10^9 \frac{q^2}{(0.01)^2} \]

Solving for \( q \):

\[ 95 = 8.9875 \times 10^9 \frac{q^2}{0.0001} \]

\[ 95 = 8.9875 \times 10^{13} q^2 \]

\[ q^2 = \frac{95}{8.9875 \times 10^{13}} \]

\[ q^2 \approx 1.057 \times 10^{-12} \]

\[ q \approx \sqrt{1.057 \times 10^{-12}} \]

\[ q \approx 1.028 \times 10^{-6} \, \text{C} \]

So, the magnitude of each charge is approximately \( 1.028 \times 10^{-6} \, \text{C} \) (or \( 1.028 \, \mu\text{C} \)).

Would you like any additional details or have any questions?

Here are 8 related questions you might find interesting:

1. How would the force change if the charges were doubled?
2. What would happen to the force if the distance between the charges was halved?
3. How does Coulomb's law compare to the gravitational law?
4. What are some practical applications of Coulomb's law?
5. How would the force change if one charge was positive and the other was negative?
6. What is the significance of Coulomb's constant in electrostatics?
7. Can Coulomb's law be applied to non-point charges?
8. What are some limitations of Coulomb's law in real-world scenarios?

**Tip:** Always ensure that units are consistent when applying physical laws to avoid calculation errors.

Learn how to determine the magnitude of two identical charges separated by a distance of 0.01m using Coulomb's Law. Includes step-by-step calculations and explanations. Suitable for advanced high school students.

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