# Electric potential energy formula

The electric potential energy formula, denoted as UE = k [q1 q2] ÷ r, establishes a relationship between the electric potential energy (UE) of a system, the Coulomb’s constant (k), the quantities of charges (q1 and q2), and the separation distance (r). This formula allows for the calculation of the electric potential energy based on the given values of charge quantities and their separation distance.

Contents

## Practice problems

### Problem #1

Calculate the electric potential energy of a system consisting of two balls, labeled 1 and 2, with charges of 15 µC and 35 µC respectively. The balls are separated by a distance of 2 m. Use a value of Coulomb’s constant, k = 8.98 × 109 N m2/C2.

Solution

Given data:

• Electric potential energy of the system, UE = ?
• Quantity of charge on ball 1, q1 = 15 µC = 15 × 10-6 C
• Quantity of charge on ball 2, q2 = 35 µC = 35 × 10-6 C
• Distance between the two charged balls, r = 2 m
• Coulomb’s constant, k = 8.98 × 109 N m2/C2

Applying the formula:

• UE = k [q1 q2] ÷ r
• UE = [(8.98 × 109) × (15 × 10-6) × (35 × 10-6)] ÷ 2
• UE = [8.98 × 15 × 35 × 10-3] ÷ 2
• UE = 4.7145 ÷ 2
• UE = 2.35 N

Therefore, the electric potential energy of the system is 2.35 N.

### Problem #2

Two spheres, labeled 1 and 2, have charges q1 = 12 µC and q2 = 24 µC respectively. They are separated by a distance of 1 m. Find the electric potential energy of the system using a value of Coulomb’s constant, k = 8.98 × 109 N m2/C2.

Solution

Given data:

• Quantity of charge on sphere 1, q1 = 12 µC = 12 × 10-6 C
• Quantity of charge on sphere 2, q2 = 24 µC = 24 × 10-6 C
• Distance between the two charged spheres, r = 1 m
• Electric potential energy of the system, UE = ?
• Coulomb’s constant, k = 8.98 × 109 N m2/C2

Applying the formula:

• UE = k [q1 q2] ÷ r
• UE = [(8.98 × 109) × (12 × 10-6) × (24 × 10-6)] ÷ 1
• UE = [8.98 × 12 × 24 × 10-3] ÷ 1
• UE = 2.58 N

Therefore, the electric potential energy of the system is 2.58 N.

### Problem #3

Determine the electric potential energy of a system in which two particles, A and B, have charges of 14 µC and 18 µC respectively. The particles are separated by a distance of 3 m. Use a value of Coulomb’s constant, k = 8.98 × 109 N m2/C2.

Solution

Given data:

• Electric potential energy of the system, UE = ?
• Quantity of charge on particle A, q1 = 14 µC = 14 × 10-6 C
• Quantity of charge on particle B, q2 = 18 µC = 18 × 10-6 C
• Distance between the two charged particles, r = 3 m
• Coulomb’s constant, k = 8.98 × 109 N m2/C2

Applying the formula:

• UE = k [q1 q2] ÷ r
• UE = [(8.98 × 109) × (14 × 10-6) × (18 × 10-6)] ÷ 3
• UE = [8.98 × 14 × 18 × 10-3] ÷ 3
• UE = 2.2629 ÷ 3
• UE = 0.75 N

Therefore, the electric potential energy of the system is 0.75 N.

### Problem #4

Calculate the electric potential energy of a system in which two masses, labeled m1 and m2, have charges of 13 µC and 16 µC respectively. The masses are separated by a distance of 1.5 m. Use a value of Coulomb’s constant, k = 8.98 × 109 N m2/C2.

Solution

Given data:

• Electric potential energy of the system, UE = ?
• Quantity of charge on mass m1, q1 = 13 µC = 13 × 10-6 C
• Quantity of charge on mass m2, q2 = 16 µC = 16 × 10-6 C
• Distance between the two charged masses, r = 1.5 m
• Coulomb’s constant, k = 8.98 × 109 N m2/C2

Applying the formula:

• UE = k [q1 q2] ÷ r
• UE = [(8.98 × 109) × (13 × 10-6) × (16 × 10-6)] ÷ 1.5
• UE = [8.98 × 13 × 16 × 10-3] ÷ 1.5
• UE = 1.8678 ÷ 1.5
• UE = 1.24 N

Therefore, the electric potential energy of the system is 1.24 N.