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Electric potential energy is the energy required to move a charge against an electric field. In simpler terms, when a charged particle is moved against the direction of the electric field, work needs to be done to overcome the natural push of electric forces in the field. This work done results in the accumulation of electric potential energy in the charged particle. The measure of this energy is in joules, and it depends on the arrangement of charges within a system, whether it’s the charge’s own or its position relative to other charged objects.
The term “electric potential energy” is specifically used in systems with changing electric fields, while “electrostatic potential energy” is designated for systems with constant fields. For instance, in a system of charged points, it represents the work needed to bring them together from infinite distance, overcoming their natural repulsion. Similarly, the electric potential energy of a specific charge or charges is the total work done by an external agent, such as applying force, moving them from infinity to their current configuration without acceleration.
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.
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.
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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.
