4. If the distance between two point charges is tripled, the mutual force between them will be changed by what factor?

ans: 1/9; force proportional to 1/d squared.

6. Two point charges, separated by 1.5 cm, have charge values of +2.0 and -4.0 µC, respectively. What is the value of the mutual force between them? (k = 9 x10⁹)

ans: 320 N; force = k*q1*q2/d*d, all in SI units.

7. An electron with a charge value of -1.6 x10^-19 C, is in the presence of an electric field of 400 N/C. What force does the electron experience?

ans: 6.4 x10^-17 N; force = q*E.

8. A ping pong ball covered with a conducting graphite coating has a mass of 0.005 kg and a charge of 4 µC. What electric field directed upward will exactly balance the weight of the ball? (g = 9.8 m/s²)

ans: 12,000 N/C; solve m*g = q*E for E.

9. The average distance of the electron from the proton in the hydrogen atom is 0.51 x10^-10m. What is the electric field from the proton's charge at the location of the electron? (k = 9 x10⁹ N m²/C², q_e = 1.6 x10^-19 C)

ans: 5.5 x10¹¹ N/C; E = k*q/d*d.

10. Two identical iron spheres have 1 mole (6 x10²³) of iron atoms each, and equal positive charges. The force between them when they are 1 m apart is 1 N. If each atom provides one free electron to the metal, what percentage of the free electrons have been removed from each sphere? (k = 9 x10⁹ N m²/C², q_e = 1.6 x10^-19 C)

ans: 1 x10^-8; use f=k*q*q/d*d to find the charge q. Then divide q by q_e to find the number of electrons.

11. If a conductor is in electrostatic equilibrium near an electrical charge:

a. the total charge on the conductor must be zero.
b. the electric field inside the conductor must be zero.
c. any charges on the conductor must be uniformly distributed.
d. the sum of all forces between the conductor and the charge must be zero.

12. In X-ray machines, electrons are subjected to electric fields as great as 6 x10⁵ N/C. Find an electron's acceleration in this field. (m_e = 9.1 x10^-31 kg, q_e = -1.6 x10^-19 C)

ans: 1.05 x10¹⁷ m/s²; acc = force/mass =q*E/m.

13. In Millikan's oil drop experiment, if the electric field between two plates is of just the right magnitude, it would exactly balance the weight of the drop. Suppose a tiny spherical oil droplet of radius 1.6 x10^-4 cm carries a single electric charge. What electric field is required to balance the weight? (The density of oil is 0.85 gram/cm³)

ans: 8.93 x10⁵ N/C; similar to ping-pong ball problem; m*g = q*E, where m = density*volume of oil drop.