1. **State the problem:** We have two charged spheres with charges $q_1 = 6$ C and $q_2 = -12$ C separated by a distance $r = 50000$ m. We need to find the electrostatic force between them.
2. **Formula used:** The electrostatic force between two point charges is given by Coulomb's law:
$$F = k \frac{|q_1 q_2|}{r^2}$$
where $k = 8.99 \times 10^9$ N m$^2$/C$^2$ is Coulomb's constant.
3. **Calculate the force:**
$$F = 8.99 \times 10^9 \times \frac{|6 \times (-12)|}{(50000)^2}$$
4. **Simplify the numerator:**
$$|6 \times (-12)| = 72$$
5. **Calculate the denominator:**
$$50000^2 = 2.5 \times 10^9$$
6. **Substitute values:**
$$F = 8.99 \times 10^9 \times \frac{72}{2.5 \times 10^9}$$
7. **Simplify the fraction:**
$$F = 8.99 \times 10^9 \times \cancel{\frac{72}{2.5 \times 10^9}} = 8.99 \times \cancel{10^9} \times \frac{72}{2.5 \times \cancel{10^9}}$$
8. **Calculate the fraction:**
$$\frac{72}{2.5} = 28.8$$
9. **Calculate the force:**
$$F = 8.99 \times 28.8 = 258.912$$
10. **Final answer:**
The magnitude of the electrostatic force between the spheres is approximately
$$F \approx 259 \text{ N}$$
The force is attractive because the charges have opposite signs.
Electrostatic Force 07B9Bf
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