Q: A uranium-238 nucleus splits into two spheres, each with $$46$$ protons and radius $$5.9 \times 10$$^{-15}$$\ \text{m}. $$What is the magnitude of the repulsive force between the two spheres immediately after fission?

$$3.5 \times 10$$^{3}$$\ \text{N}$$

Q: Two small positively charged spheres have a combined charge of $$5.0 \times 10$$^{-5}$$\ \text{C}. If $$they repel each other with a force of $$1.0\ \text{N}$$ when $$2.0\ \text{m}$$ apart, what are the individual charges?

One sphere has $$1.16 \times 10$$^{-5}$$\ \text{C}$$ and the other $$3.84 \times 10$$^{-5}$$\ \text{C}$$

Q: Two identical conducting spheres, fixed in place, initially attract each other with a force of $$0.108\ \text{N}$$ when separated by $$0.500\ \text{m}. $$After being connected by a wire and then separated, they repel each other with a force of $$0.0360\ \text{N}. $$What are the possible initial charges on the spheres?

One sphere has $$+3.00\ \mu\text{C}$$ and the other $$-1.00\ \mu\text{C}$$, or vice versa; or $$+1.00\ \mu\text{C}$$ and $$-3.00\ \mu\text{C}$$, or vice versa.

Q: If $$6.2 \times 10$$^{11}$$ electrons are removed from a penny, what is the resulting charge on the penny?

$$+1.0 \times 10$$^{-7}$$\ \text{C}$$

Question 1

Which of the following statements best describes the concept of electric charge quantization?

Accepted Answer

Electric charge exists only in integral multiples of the elementary charge $$e$$, i.e., $$q = ne$$ where $$n = 0, \pm1, \pm2, \ldots$$

Question 2

A copper penny with a mass of 3.11 g is made entirely of copper. If each copper atom contains 29 electrons, what is the approximate total number of electrons in the penny?

Accepted Answer

$$8.55 	imes 10$$^{23}$$

Question 3

Which of the following best explains why two identical conducting spheres, after being connected by a wire, have equal charges?

Accepted Answer

Charge redistributes itself evenly between identical conductors due to their symmetry and equal capacity.

Question 4

Two point charges, $$q_1 = +3.00$$ 	imes $$10^{-6}$$\ 	ext{C}$$ and q_2$ = -1.50 	imes 10$$^{-6}$$\ 	ext{C}$$, are separated by $$12.0\ 	ext{cm}. $$What is the magnitude of the force between them?

Accepted Answer

$$2.81\ 	ext{N}$$

Question 5

A uranium-238 nucleus splits into two spheres, each with $$46$$ protons and radius $$5.9 	imes 10$$^{-15}$$\ 	ext{m}. $$What is the magnitude of the repulsive force between the two spheres immediately after fission?

Accepted Answer

$$3.5 	imes 10$$^{3}$$\ 	ext{N}$$

Question 6

If a certain charge $$Q is $$divided into two parts $$q$$ and $$Q-q$$, and separated by a fixed distance, what value of $$q$$ maximizes the electrostatic repulsion between the two charges?

Accepted Answer

$$q = \frac{Q}{2}$$

Question 7

Two small positively charged spheres have a combined charge of $$5.0 	imes 10$$^{-5}$$\ 	ext{C}. If $$they repel each other with a force of $$1.0\ 	ext{N}$$ when $$2.0\ 	ext{m}$$ apart, what are the individual charges?

Accepted Answer

One sphere has $$1.16 	imes 10$$^{-5}$$\ 	ext{C}$$ and the other $$3.84 	imes 10$$^{-5}$$\ 	ext{C}$$

Question 8

A neutron consists of one 'up' quark ($$+\frac{2e}{3}) $$and two 'down' quarks ($$-\frac{e}{3}$$ each). If the down quarks are $$2.6 	imes 10$$^{-15}$$\ 	ext{m}$$ apart, what is the magnitude of the electrostatic force between them?

Accepted Answer

$$3.8\ 	ext{N}$$

Question 9

Which of the following is the correct expression for Coulomb's Law in terms of the permittivity constant $$\$$epsilon_0$$?

Accepted Answer

$$F = \frac{1}{4\pi\$$epsilon_0$$} \frac{|q_1$||q_2$|}{r^2$}$$

Question 10

A point charge $$q_1 = 26.0$$\ \mu	ext{C}$$ and q_2$ = -47.0\ \mu	ext{C}$$ are separated by a distance $$r$$ such that the force between them is $$5.70\ 	ext{N}. $$What is the value of $$r$$?

Accepted Answer

$$1.39\ 	ext{m}$$

Question 11

Which of the following best describes the superposition principle for electric forces?

Accepted Answer

The total force on a charge is the sum of the individual forces from all other charges, calculated using Coulomb's Law.

Question 12

A wire carries a current of $$1\ 	ext{A}. $$How much charge passes a given point in the wire in $$1\ 	ext{s}$$?

Accepted Answer

$$1\ 	ext{C}$$

Question 13

Two identical conducting spheres, fixed in place, initially attract each other with a force of $$0.108\ 	ext{N}$$ when separated by $$0.500\ 	ext{m}. $$After being connected by a wire and then separated, they repel each other with a force of $$0.0360\ 	ext{N}. $$What are the possible initial charges on the spheres?

Accepted Answer

One sphere has $$+3.00\ \mu	ext{C}$$ and the other $$-1.00\ \mu	ext{C}$$, or vice versa; or $$+1.00\ \mu	ext{C}$$ and $$-3.00\ \mu	ext{C}$$, or vice versa.

Question 14

A charge $$q_1 = +3.0$$\ \mu	ext{C}$$ is located at (3.5$$\ 	ext{cm}, 0.50\ 	ext{cm})$$ and q_2$ = -4.0\ \mu	ext{C} at$$ $$(-2.0\ 	ext{cm}, 1.5\ 	ext{cm}). $$What is the magnitude of the force on $$q_2$$ due to $$q_1$$?

Accepted Answer

$$35\ 	ext{N}$$

Question 15

Which of the following materials is classified as a conductor?

Accepted Answer

Copper

Question 16

If $$6.2 	imes 10$$^{11}$$ electrons are removed from a penny, what is the resulting charge on the penny?

Accepted Answer

$$+1.0 	imes 10$$^{-7}$$\ 	ext{C}$$

Question 17

Which of the following is NOT a consequence of Coulomb's Law?

Accepted Answer

The force is always perpendicular to the line joining the charges.

Question 18

In a real-world scenario, why is the force between two charged spheres after nuclear fission so large compared to everyday electrostatic forces?

Accepted Answer

Because the spheres have a large number of protons and are extremely close together, resulting in a large product of charges and a small separation distance in Coulomb's Law.

Electric Charge and Coulomb’s Law: Concepts, Properties, and Applications

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