**Update:** This page’s content is moving to a new address in the upcoming months.

The **electric potential energy formula**, denoted as U_{E} = k [q_{1} q_{2}] ÷ r, establishes a relationship between the electric potential energy (U_{E}) of a system, the Coulomb’s constant (k), the quantities of charges (q_{1} and q_{2}), 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.

## 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 × 10^{9} N m^{2}/C^{2}.

**Solution**

Given data:

- Electric potential energy of the system, U
_{E}= ? - Quantity of charge on ball 1, q
_{1}= 15 µC = 15 × 10^{-6}C - Quantity of charge on ball 2, q
_{2}= 35 µC = 35 × 10^{-6}C - Distance between the two charged balls, r = 2 m
- Coulomb’s constant, k = 8.98 × 10
^{9}N m^{2}/C^{2}

Applying the formula:

- U
_{E}= k [q_{1}q_{2}] ÷ r - U
_{E}= [(8.98 × 10^{9}) × (15 × 10^{-6}) × (35 × 10^{-6})] ÷ 2 - U
_{E}= [8.98 × 15 × 35 × 10^{-3}] ÷ 2 - U
_{E}= 4.7145 ÷ 2 - U
_{E}= 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 q_{1} = 12 µC and q_{2} = 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 × 10^{9} N m^{2}/C^{2}.

**Solution**

Given data:

- Quantity of charge on sphere 1, q
_{1}= 12 µC = 12 × 10^{-6}C - Quantity of charge on sphere 2, q
_{2}= 24 µC = 24 × 10^{-6}C - Distance between the two charged spheres, r = 1 m
- Electric potential energy of the system, U
_{E}= ? - Coulomb’s constant, k = 8.98 × 10
^{9}N m^{2}/C^{2}

Applying the formula:

- U
_{E}= k [q_{1}q_{2}] ÷ r - U
_{E}= [(8.98 × 10^{9}) × (12 × 10^{-6}) × (24 × 10^{-6})] ÷ 1 - U
_{E}= [8.98 × 12 × 24 × 10^{-3}] ÷ 1 - U
_{E}= 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 × 10^{9} N m^{2}/C^{2}.

**Solution**

Given data:

- Electric potential energy of the system, U
_{E}= ? - Quantity of charge on particle A, q
_{1}= 14 µC = 14 × 10^{-6}C - Quantity of charge on particle B, q
_{2}= 18 µC = 18 × 10^{-6}C - Distance between the two charged particles, r = 3 m
- Coulomb’s constant, k = 8.98 × 10
^{9}N m^{2}/C^{2}

Applying the formula:

- U
_{E}= k [q_{1}q_{2}] ÷ r - U
_{E}= [(8.98 × 10^{9}) × (14 × 10^{-6}) × (18 × 10^{-6})] ÷ 3 - U
_{E}= [8.98 × 14 × 18 × 10^{-3}] ÷ 3 - U
_{E}= 2.2629 ÷ 3 - U
_{E}= 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 m_{1} and m_{2}, 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 × 10^{9} N m^{2}/C^{2}.

**Solution**

Given data:

- Electric potential energy of the system, U
_{E}= ? - Quantity of charge on mass m
_{1}, q_{1}= 13 µC = 13 × 10^{-6}C - Quantity of charge on mass m
_{2}, q_{2}= 16 µC = 16 × 10^{-6}C - Distance between the two charged masses, r = 1.5 m
- Coulomb’s constant, k = 8.98 × 10
^{9}N m^{2}/C^{2}

Applying the formula:

- U
_{E}= k [q_{1}q_{2}] ÷ r - U
_{E}= [(8.98 × 10^{9}) × (13 × 10^{-6}) × (16 × 10^{-6})] ÷ 1.5 - U
_{E}= [8.98 × 13 × 16 × 10^{-3}] ÷ 1.5 - U
_{E}= 1.8678 ÷ 1.5 - U
_{E}= 1.24 N

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

## Related

- Thermal energy equation
- Potential energy formula
- Gravitational potential energy formula
**Electric potential energy formula**- Elastic potential energy formula
- Kinetic energy formula
- Rotational kinetic energy formula
- Electrical energy equation
- Mechanical energy formula
- Photon energy equation
- Conservation of energy formula

## External links

- https://study.com/learn/lesson/electric-potential-energy-formula-examples.html
- https://sciencing.com/calculate-electric-potential-energy-7821281.html

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.