Answer to Question #309908 in Physics for jovie

Question

1. Two small conducting and identical spheres A and B have charges -32nC and +20nC respectively, they are separated by a distance of 0.23m.

a. What is the magnitude of the electric force between two spheres? Is this force attractive or repulsive?

b. What is the magnitude of the gravitational force between two spheres? Is this force attractive or repulsive?

2. Two protons are separated by a distance of 2.3×10^-10m in air.

a. Find the magnitude of electric force one proton exerts on the other. Is this force attractive or repulsive?

b. Find the magnitude of the gravitational force one proton exerts on the other. Is this force attractive or repulsive?

Answer 1

1a. The magnitude of the electric force is:

$$F = k\dfrac{|q_1q_2|}{r^2}\\ F = 9\times 10^9\cdot \dfrac{32\times 10^{-9}\cdot 20\times 10^{-9}}{0.23^2} \approx 1.1\times 10^{-4}N$$

The force is attractive, since the charges have opposite signs.

1b. The magnitude of the gravitational force can not be found, since it depends on the masses of the spheres. Gravitaional force is always attractive.

2a. The electric force (repulsive, since protons are both positively charged):

$$F = k\dfrac{e^2}{r^2} = 9\times 10^9\cdot\dfrac{(1.6\times 10^{-19})^2}{(3.6\times 10^{10})^2}\approx 1.8\times 10^{-49}N$$

2b. The gravitational force (always attractive):

$$F = G\dfrac{m^2}{r^2} = 6.67\times 10^{-11}\cdot \dfrac{(1.67\times 10^{-27})^2}{(3.6\times 10^{10})^2}\approx 1.4\times 10^{-85}N$$