# Coulomb’s law equation

The Coulomb’s law equation, F = k [q1 q2] ÷ r2, states that the electric force (F) between two charged objects depends directly on the magnitude of their charges (q1 and q2) and inversely on the square of the distance (r) between them. This equation allows for the calculation of the electric force between two charged objects by taking into account their charges and the distance separating them.

Contents

## Practice problems

### Problem #1

Calculate the electric force between two charged balls, ball 1 and ball 2, which have charges of 12 µC and 16 µC, respectively. The balls are separated by a distance of 1 m. Use the value of Coulomb’s constant, k = 8.98 × 109 N m2/C2.

Solution

Given data:

• Electric force acting between two charged balls, F = ?
• Quantity of charge on ball 1, q1 = 12 µC = 12 × 10-6 C
• Quantity of charge on ball 2, q2 = 16 µC = 16 × 10-6 C
• Distance between the two charged balls, r = 1 m
• Coulomb’s constant, k = 8.98 × 109 N m2/C2

Applying the formula:

• F = k [q1 q2] ÷ r2
• F = [(8.98 × 109) × (12 × 10-6) × (16 × 10-6)] ÷ (1)2
• F = [8.98 × 12 × 16 × 10-3] ÷ 1
• F = 1724.16 × 10-3
• F = 1.72 N

Therefore, the electric force acting between two charged balls is 1.72 N.

### Problem #2

Two metal spheres with charges of 25 µC and 6 µC are separated by a distance of 1.1 m. Determine the magnitude of the electric force between these charged spheres, using the value of Coulomb’s constant, k = 8.98 × 109 N m2/C2.

Solution

Given data:

• Quantity of charge on sphere 1, q1 = 25 µC = 25 × 10-6 C
• Quantity of charge on sphere 2, q2 = 6 µC = 6 × 10-6 C
• Distance between the two charged spheres, r = 1.1 m
• Electric force acting between two charged spheres, F = ?
• Coulomb’s constant, k = 8.98 × 109 N m2/C2

Applying the formula:

• F = k [q1 q2] ÷ r2
• F = [(8.98 × 109) × (25 × 10-6) × (6 × 10-6)] ÷ (1.1)2
• F = [8.98 × 25 × 6 × 10-3] ÷ 1.21
• F = 1113.22 × 10-3
• F = 1.11 N

Therefore, the electric force acting between two charged spheres is 1.11 N.

### Problem #3

Two charged objects with charges of q1 = 3 µC and q2 = 9 µC are separated by a distance of 2 m. If the value of Coulomb’s constant is k = 8.98 × 109 N m2/C2, calculate the electric force between these two charged objects.

Solution

Given data:

• Quantity of charge on an object 1, q1 = 3 µC = 3 × 10-6 C
• Quantity of charge on an object 2, q2 = 9 µC = 9 × 10-6 C
• Distance between the two charged objects, r = 2 m
• Coulomb’s constant, k = 8.98 × 109 N m2/C2
• Electric force acting between two charged objects, F = ?

Applying the formula:

• F = k [q1 q2] ÷ r2
• F = [(8.98 × 109) × (3 × 10-6) × (9 × 10-6)] ÷ (2)2
• F = [8.98 × 3 × 9 × 10-3] ÷ 4
• F = 60.615 × 10-3
• F = 6.06 × 10-2 N

Therefore, the electric force acting between two charged objects is 6.06 × 10-2 N.

### Problem #4

Calculate the electric force between two charged balloons separated by a distance of 1.4 m. The balloons have charges of q1 = 14 µC and q2 = 20 µC. Use the value of Coulomb’s constant, k = 8.98 × 109 N m2/C2.

Solution

Given data:

• Electric force acting between two charged balloons, F = ?
• Distance between the two charged balloons, r = 1.4 m
• Quantity of charge on balloon 1, q1 = 14 µC = 14 × 10-6 C
• Quantity of charge on balloon 2, q2 = 20 µC = 20 × 10-6 C
• Coulomb’s constant, k = 8.98 × 109 N m2/C2

Applying the formula:

• F = k [q1 q2] ÷ r2
• F = [(8.98 × 109) × (14 × 10-6) × (20 × 10-6)] ÷ (1.4)2
• F = [8.98 × 14 × 20 × 10-3] ÷ 1.96
• F = 1282.85 × 10-3
• F = 1.28 N

Therefore, the electric force acting between two charged balloons is 1.28 N.