Coulomb’s LawAdditional Practice Problems

answers

1.

A helium nucleus has charge +2e and a neon nucleus +10e, where e = 1.60 x 10-19

C. With what force do they repel each other when separated by 3 x 10-9 meters?

1.

𝐹 =𝑘𝑞1𝑞2𝑑2

𝐹 =9 × 109 2(1.6 × 10−19) 10(1.6 × 10−19)

3 × 10−9 2

𝐹 = 5.1 x 10−10 N

2.

If two equal charges, each of 1 coulomb, were separated in air by a distance of 1 km, what would be the force between them?

2.

𝐹 =𝑘𝑞1𝑞2𝑑2

𝐹 =9 × 109 1 1

1000 2

𝐹 = 9000 N

3.

Determine the force between two free electrons spaced 1 angstrom (10-10 m) apart.

𝐹 =𝑘𝑞1𝑞2𝑑2

𝐹

=9 × 109 1.6 × 10−19 1.6 × 10−19

1 × 10−10 2

𝐹 = 2.3 × 10−8 N

3.

4.

The force of repulsion between two argon nuclei is 7.4 x 10-8 N when separated by what distance. The charge on an argon nucleus is +18e.

4.

𝐹 = 𝑘𝑞1𝑞2𝑑2

𝑑 = 𝑘𝑞1𝑞2𝐹

= (9 × 109)18(1.6 × 10−19)18(1.6 × 10−19)

7.4 × 10−8

= 1.004 × 10−9 𝑚

5.

Two equally charged pith balls are 3 cm apart in air and repel each other with a force of 4 x 10-5 N. Compute the charge on each ball.

5.

𝐹 = 𝑘𝑞1𝑞2𝑑2

→ 𝐹 = 𝑘𝑞2

𝑑2

𝑞 =𝐹𝑑2

𝑘=

(4 × 10−5)(0.03)2

9 × 109= 2 × 10−9𝐶

6.

Two small equal pith balls are 3 cm apart in air and carry charges of +3 x 10-9 and –12 x 10-9 C respectively. Compute the force of attraction.

6.

𝐹 = 𝑘𝑞1𝑞2𝑑2

= (9 × 109)3 × 10−9 −12 × 10−9

0.032

= −3.6 × 10−4 𝑁

6.

The charge will balance if the two pith balls touch.

𝑞1 = 𝑞2 =3 × 10−9 + −12 × 10−9

2= −4.5 × 10−9 C

𝐹 = 𝑘𝑞1𝑞2𝑑2

= 9 × 109−4.5 × 10−9 C

2

0.032= 2.025 × 10−4𝑁

7.

The normal hydrogen atom consists of a proton nucleus and an orbital electron, each carrying the fundamental charge of magnitude e = 1.60 x 10-19

C. Assuming that the electron orbit is circular and the separation between the particles is 5.3 x 10-11

meters, find:

a. the force of electrical attraction between the particles

7a.

𝐹 = 𝑘𝑞1𝑞2

𝑑2

= (9 × 109)1.6 × 10−19 −1.6 × 10−19

(5.3 × 10−11)2

= −8.14 × 10−8 𝑁

7b.

the gravitational force of attraction between them

𝐹 = 𝐺𝑚1𝑚2

𝑑2

= (6.67 × 10−11)1.67 × 10−27 9.11 × 10−31

5.3 × 10−11 2

= 3.61 × 10−47𝑁

7c.

which force is larger? How many times?

Obviously the electrical force.

=8.14 × 10−8 𝑁

3.61 × 10−47𝑁= 2.25 × 1039 times larger

8.

What is the net force on the sphere having charge of -4e?

8.

Find the force between the +5e and -4e

𝐹 = 𝑘𝑞1𝑞2𝑑2

= (9 × 109)−4 1.6 × 10−19 5 −1.6 × 10−19

(0.02)2

= −1.15 × 10−23 𝑁

8.

Find the force between the +2e and -4e

𝐹 = 𝑘𝑞1𝑞2𝑑2

= (9 × 109)−4 1.6 × 10−19 2 1.6 × 10−19

(0.01)2

= −1.84 × 10−23 𝑁

8.

Find the net force𝑎2 + 𝑏2 = 𝑐2

𝑐 = −1.15 × 10−23 2 + −1.84 × 10−23 2

𝑐 = 2.17 × 10−23