Exercises: Coulomb's Law

Work through each section in order. Use $k = 9 \times 10^9$ N·m²/C² throughout. Show your work on all calculation problems.

Grade 11·20 problems·~35 min·OpenStax Physics (High School)·section·sec-18-2

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Warm-Up: Prerequisite Review

These questions review concepts needed for this section.

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?

The constant $G$

The distance $r$

The masses $m_1$ and $m_2$

The force $F$

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

Attractive

Repulsive

No force — they cancel each other.

It depends on which charge is larger.

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

Both forces can only be attractive.

Both forces follow an inverse-square relationship with distance.

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

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

Fluency Practice

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

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

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

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

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

Zero — protons are too small to exert detectable forces.

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.

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.

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?

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

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

$2F$ — force doubles when distance doubles

$4F$ — 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

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.

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.

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