Two identical conducting spheres, fixed in place, attract each other with an electrostatic force of 0.110 N when their center-to-center separation is 57.3 cm. The spheres are then connected by a thin conducting wire. When the wire is removed, the spheres repel each other with an electrostatic force of 0.0489 N. Of the initial charges on the spheres, with a positive net charge, what was (a) the negative charge on one of them and (b) the positive charge on the other

  q₂ = ± 1.306 10⁻⁶ C

   q₂ =  ± 3.073 10⁻⁶ C

Explanation:

We must solve this exercise using Coulomb's law, let's write the equilibrium equation for each case

first case

     F₁ = k q₁ q₂ / r²         (1)

where F1 is the force on sphere 1, with a value of F₁ = 0.110 N; r is the distance between them r = 0.573 m

second case.

The spheres were joined with a conductive wire, so the charge of the two is equal, then the wire is removed and

       -F₂ = k q₃ q₃ / r²           (2)

In this case the force is expelling and is equal to F₂ = 0.0489 N

when the spheres are joined with the wire the charge of the spheres is distributed evenly between them two

         q₁ + q₂ = 2 q₃             (3)

we can see that there are three equations with three unknowns for which the system can be solved

let's substitute equation 3 in 2

         - F₂ = k (q₁ + q₂)² / r²

we join this equation with equation 1

          F₁ = k q₁ q₂ / r²

          -F₂ = k (q₁ + q₂)²/4r²

          q₁ = F₁ r² / k q₂

         - F₂ = k (F₁ r² / k q₂ + q₂)²/4r²

Let's replace the values and work out

         - 0.0489 = 9 109 (0.110 0.573² / (9 10⁹ q₂) + q₂)² / 0.573²

          - 0.0489 4 0.573²/9 10⁹ = (0.110 0.573² / (9 10⁹ q₂) + q₂)²

          - 7.1356 10⁻¹² = (4.013 10⁻¹² / q₂ + q₂)²

          - 7.1356 10⁻¹² = 1 / q₂² (4.013 10⁻¹² + q₂² )²

          - 7.1356 10⁻¹² q₂² = (16.104 10⁻²⁴ + 4.013 10⁻¹² q₂² + q₂⁴

          q₂⁴ + q₂² (4,013 10⁻¹² + 7,1356 10⁻¹²) + 16,104 10⁻²⁴ = 0

we change variables

        q’ = q₂²

          q'² + q'  11.1486 10⁻¹² + 16.104 10⁻²⁴ = 0

we solve this quadratic equation

          q '= [- 11.1486 10⁻¹² ±√ ((11.1486 10⁻¹² )² - 4 16.104 10⁻²⁴)] / 2

          q '= [- 11.1486 10 12 ±√ (59.8753 10⁻²⁴)] / 2

          q '= [- 11.1486 ± 7.7379] / 2 10⁻¹²

          q'1 = -1.70535 10⁻¹²

          q'2 = -9.44325 10⁻¹²

           q' = q₂²

           q₂ = √ q'

           q₂ = ± 1.306 10⁻⁶ C

           q₂ =  ± 3.073 10⁻⁶ C

since q 'is squared of these charges they can be positive or negative giving the same result.

the cellphone, they would then know if the killer would have contacted them or always hated them. or if it was a breakup. but if that is not the case, then it would be the clothing. to put in a bullet, it would have to be put in by hands. hands have finger prints which, would have giving you the answer of who done it.

explanation:

connect the batteries in series and hope