If the force of attraction between two charges is 310 N, what will be the force if one of the charges is made four times larger and the distance is reduced to half of its original value? (4.96 kN)

The force of attraction between two charges follows Coulomb's Law, which is given by:

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

Where:
- \( F \) is the force of attraction,
- \( k \) is Coulomb's constant,
- \( q_1 \) and \( q_2 \) are the charges,
- \( r \) is the distance between the charges.

We are told that initially, the force is 310 N. If one of the charges is increased by a factor of 4 and the distance is reduced to half, the new force \( F' \) can be calculated using the following steps.

### New Charge and Distance:

- One of the charges is made four times larger, so \( q'_1 = 4q_1 \).
- The distance is halved, so \( r' = \frac{r}{2} \).

### New Force Calculation:
Using Coulomb’s Law for the new scenario:

\[
F' = k \frac{(4q_1) q_2}{\left(\frac{r}{2}\right)^2}
\]

Simplifying:

\[
F' = k \frac{4q_1 q_2}{\frac{r^2}{4}} = 4 \times 4 \times k \frac{q_1 q_2}{r^2} = 16 \times F
\]

Since the original force \( F \) is 310 N, the new force is:

\[
F' = 16 \times 310 \, \text{N} = 4960 \, \text{N} = 4.96 \, \text{kN}
\]

Thus, the new force is 4.96 kN.

Would you like more details or further explanation on any part of this?

Here are five related questions:
1. What is Coulomb's constant, and how is it derived?
2. How does changing the distance affect the force between two charges?
3. How does the force change if both charges are doubled?
4. What happens to the force if the distance is tripled but the charges remain the same?
5. How does this scenario relate to gravitational attraction?

**Tip:** When solving problems involving forces between charges, always focus on how changes in charge and distance scale the force based on Coulomb's law.

Understand how to calculate the force between two charges using Coulomb's Law. In this example, one charge is made four times larger and the distance is halved. Explore how the force changes from 310 N to 4.96 kN with step-by-step calculations. Suitable for students in Grades 10-12.

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