Physics highshool level

Question

There are three equally sized positively charged metal spheres. Sphere A is 2.00 m left of sphere B, and sphere C is 1.5 m right of sphere B. sphere A has quadruple the charge of Sphere B, and sphere C has half the charge of sphere A. If the force exerted on sphere A by sphere C is 45.0 N, what is the charge of Sphere B, in Coulombs?

Answer 1

Oh, this is a fun one! I like the little riddle in the beginning. Let's sort out the information, define some terms and rock this!

1. From the problem we know the following is true:
2. Sphere A -- 2m -- Sphere B --1.5 --Sphere C
3. Charge of A = 4B
4. Charge of C= A/2
5. Our question is: If the force exerted on sphere A by sphere C is 45.0 N, what is the charge of Sphere B, in Coulombs? Coulomb's law states:
6. F= force (45)
7. k= constant (8.98755 × 10⁹ kg/m³ ) I am going to round to 9 × 10⁹ kg/m³ for simplicity
8. q₁= A's charge
9. q₂= C's charge (which is q₁/2)
10. r = space between the objects (3.5m)
11. 45 = (9 × 10⁹ kg/m³ ) (A(.5A) / 3.5²)
12. Now we solve the problem to get the answer for A's charge.
13. 45/(9 × 10⁹ kg/m³) = (A(.5A) / 3.5²)
14. 5 x 10^-8 = (A(.5A) / 3.5²)
15. (5 x 10^-8) (3.5²) = A(.5A)
16. 6.125 x 10^-8 = 1A (.5A)
17. 6.125 x 10^-8 = .5A
18. (2)6.125 x 10^-8 = .5A (2)
19. 1.225 x 10^-7 = A
20. Remember that A =4B so (4) 1.225 x 10^-7 = 4.9 x 10^-7

If your teacher/professor does not simplify the constant plug in 8.98755 × 10⁹ kg/m³ where you see 9 x 10⁹.