Question

5. Two identical metal spheres are placed 15.0 cm apart. A charge of 6.00 µC is placed on one sphere while a charge of −2.00 µC is placed upon the other. What is the force on each sphere? If the two spheres are brought together and touched and then separated to their original separation, what will be the force on each sphere?

Answer: F₁₂ =4.80 N attractive     q = 2.00 μC           F₁₂ = 1.60 N repulsive

7. Three charges q1 = 2.00 µC, q2 = 5.00 µC, and q3 = 8.00 µC are placed along the x-axis at 0.00, 45.0 cm, and 72.4 cm respectively. Find the force on each charge.

Answer: F3= 5.08

Step by step would be great so I can understand this better.

Answer 1

5.
a) The force between the two spheres is F = k q1 q2 / r²
The distance between the spheres, r = 15.0 cm = 0.15 m
q1 = 6.00 C, q2 = - 2.00 C
The force F = 9 x 10⁹ x 6.00 x 10^-6 C x 2.00 x 10^-6 C / (0.15 m)²
F = 4.8 N
Since the spheres are oppositively charged, the force between them is attractive.
b ) The total charge on each sphere is after being brought together and touched,
q = q1 + q2 / 2 = 6.00   C - 2.00 C / 2 = 2.00 C
The froce between the spheres
F =k q² / r²
F = 9 x 10⁹ x ( 2.00 x 10^-6 C )² / 0.15²
F = 1.6 N