Subjects physics

Electrostatic Force 07B9Bf

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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.