Task Sets: Coulomb's Law - OpenStax Physics (High School)

A

Warm-Up: Prerequisite Review

These questions review concepts needed for this section.

1.

Newton's Law of Gravitation is $F = \frac{Gm_1 m_2}{r^2}$ . Which term in this formula plays the same role as the charges in Coulomb's Law?

A.

The constant $G$

B.

The distance $r$

C.

The masses $m_1$ and $m_2$

D.

The force $F$

2.

Two charges of the same sign are brought close together. What type of electric force acts between them?

A.

Attractive

B.

Repulsive

C.

No force — they cancel each other.

D.

It depends on which charge is larger.

3.

Which feature do Coulomb's Law and Newton's Law of Gravitation share?

A.

Both forces can only be attractive.

B.

Both forces follow an inverse-square relationship with distance.

C.

Both use the same constant ( $k = G$ ).

D.

Both forces are equal in magnitude for the same pair of objects.

B

Fluency Practice

Use $k = 9 \times 10^9$ N·m²/C². Show your work and state the direction of each force.

1.

Two protons are separated by a distance $r$ . Which of the following correctly describes the electric force between them?

A.

Attractive, with magnitude $F = \frac{k e^2}{r^2}$

B.

Repulsive, with magnitude $F = \frac{k e^2}{r^2}$

C.

Attractive, with magnitude $F = \frac{k e}{r^2}$

D.

Zero — protons are too small to exert detectable forces.

2.

Calculate the magnitude of the electric force between two charges: $q_1 = +3 \times 10^{-6}$ C and $q_2 = +5 \times 10^{-6}$ C, separated by $r = 0.30$ m. Express your answer in newtons to two significant figures.

3.

Calculate the magnitude of the electric force between $q_1 = +2 \times 10^{-6}$ C and $q_2 = -4 \times 10^{-6}$ C separated by $r = 0.20$ m. Express your answer in newtons to two significant figures.

4.

The electric force between two charges separated by distance $r$ is $F$ . If the distance is doubled to $2r$ (charges unchanged), what is the new force?

A.

$\frac{F}{2}$ — distance doubled, force halved

B.

$\frac{F}{4}$ — distance doubled, force reduced by factor of 4

C.

$2F$ — force doubles when distance doubles

D.

$4F$ — force quadruples when distance doubles

A number line showing three charges: A (+4 μC) at 0 m, B (−2 μC) at 0.30 m, and C (+3 μC) at 0.50 m

5.

Three charges are on a line. Charge A ( $+4 \mu$ C) is at position 0, charge B ( $-2 \mu$ C) is at 0.30 m, and charge C ( $+3 \mu$ C) is at 0.50 m. Find the net force on charge B.

Taking rightward as positive, what is the net force on B in newtons? (Positive = right, negative = left.) Express your answer to two significant figures.

6.

In the same setup (A at 0, B at 0.30 m, C at 0.50 m), what is the net force on charge C? (Positive = right, negative = left.) Express your answer to two significant figures.

C

Mixed Practice

These problems apply Coulomb's Law concepts in varied formats.

D

Application Problems

Read each scenario carefully and show your work.

1.

A charge of $q_1 = +5.0 \times 10^{-9}$ C is placed 0.15 m from a charge of $q_2 = -3.0 \times 10^{-9}$ C.

Calculate the magnitude of the electric force between the two charges. Express your answer in newtons to two significant figures.

2.

A proton (mass $m_p = 1.67 \times 10^{-27}$ kg, charge $+e = +1.6 \times 10^{-19}$ C) and an electron (mass $m_e = 9.11 \times 10^{-31}$ kg, charge $-e$ ) are separated by $r = 5.3 \times 10^{-11}$ m (a typical atomic distance).

1.

Calculate the magnitude of the electric force between the proton and electron. Express your answer in newtons to two significant figures.

2.

The gravitational force between the proton and electron at the same distance is approximately $3.6 \times 10^{-47}$ N. What does the ratio of electric to gravitational force tell us about physics at the atomic scale?

A.

Gravity is comparable to the electric force — both matter at atomic scales.

B.

The electric force is roughly $10^{39}$ times stronger than gravity — gravity is completely negligible at atomic scales.

C.

The forces are equal — the numbers are just different units.

D.

Gravity is stronger than the electric force inside the atom.

3.

Three charges are on a line: $q_1 = +2 \mu$ C at $x = 0$ , $q_2 = -2 \mu$ C at $x = 0.10$ m, $q_3 = +2 \mu$ C at $x = 0.20$ m.

Without calculating exact numbers, predict the direction of the net force on $q_2$ . Explain your reasoning using the superposition principle and the attractive/repulsive nature of each pair.

E

Find the Mistake

Each problem shows an error in applying Coulomb's Law. Identify the mistake.

1.

A student calculates the electric force on a $+3$ μC charge placed 0.5 m from a $-6$ μC charge:
$F = \frac{k q_1}{r^2} = \frac{(9 \times 10^9)(3 \times 10^{-6})}{(0.5)^2} = 0.108 \text{ N}$

What error did the student make?

A.

The student used the wrong value for $k$ .

B.

The student omitted the second charge — Coulomb's Law requires the product of both charges.

C.

The student should have used $r$ instead of $r^2$ .

D.

The student should have used the sum of the charges, not the product.

2.

A student is given: charge A = $+8$ μC and charge B = $+2$ μC, separated by 0.4 m. The student concludes: "Charge A feels a larger electric force because it has more charge. Charge B feels less force because it is smaller."

What is wrong with this student's reasoning?

A.

The student correctly identified that larger charges feel stronger forces.

B.

Newton's Third Law requires the forces on A and B to be equal in magnitude — the formula $F = k|q_A q_B|/r^2$ is symmetric and gives the same value for both charges.

C.

Charge B feels zero force because it is smaller.

D.

Charge A feels a smaller force because it repels charge B more strongly.

F

Challenge Problem

This bonus problem requires multi-step reasoning.

Number line showing q₁ (−6 μC) at 0 m, q₂ (+4 μC) at 0.20 m, and q₃ (−3 μC) at 0.50 m, with distances labeled

1.

Three charges on a line: $q_1 = -6 \mu$ C at $x = 0$ , $q_2 = +4 \mu$ C at $x = 0.20$ m, $q_3 = -3 \mu$ C at $x = 0.50$ m. Find the net force on $q_2$ .