Force Change A354D2
1. **Problem statement:** We have two opposite charges with the same magnitude $q$ separated by a distance $r$, producing a force $F$ between them.
2. **Formula used:** The force between two point charges is given by Coulomb's law:
$$F = k \frac{|q_1 q_2|}{r^2}$$
where $k$ is Coulomb's constant, $q_1$ and $q_2$ are the charges, and $r$ is the distance between them.
3. **Initial condition:** Both charges have magnitude $q$, so the initial force is:
$$F = k \frac{q \times q}{r^2} = k \frac{q^2}{r^2}$$
4. **After transfer:** 60% of the charge from one is transferred to the other.
- Charge on first becomes $q_1 = q - 0.6q = 0.4q$
- Charge on second becomes $q_2 = q + 0.6q = 1.6q$
5. **New force:**
$$F' = k \frac{|q_1 q_2|}{r^2} = k \frac{0.4q \times 1.6q}{r^2} = k \frac{0.64 q^2}{r^2}$$
6. **Change in force:**
$$\frac{F'}{F} = \frac{0.64 q^2 / r^2}{q^2 / r^2} = 0.64$$
7. **Interpretation:** The force becomes 64% of the original force, so it decreases by 36%.