
The electric force equation, based on Coulomb’s law, allows us to calculate the force between two charged objects. It is expressed as Fe = k [q1 q2] ÷ r2, where Fe represents the electric force, k is the Coulomb’s constant, q1 and q2 are the charges of the objects, and r is the distance between the two charged objects.
Practice problems
Problem #1
Calculate the electric force acting between two objects, object 1 and object 2, with charges of 20 µC and 15 µC, respectively, separated by a distance of 1 m. Take the value of the proportionality constant, k, as 8.98 × 109 N m2/C2.
Solution
Given data:
- Electric force acting between two charged objects, Fe = ?
- Quantity of charge on object 1, q1 = 20 µC = 20 × 10-6 C
- Quantity of charge on object 2, q2 = 15 µC = 15 × 10-6 C
- Distance between the two charged objects, r = 1 m
- Proportionality constant, k = 8.98 × 109 N m2/C2
Applying the formula:
- Fe = k [q1 q2] ÷ r2
- Fe = [(8.98 × 109) × (20 × 10-6) × (15 × 10-6)] ÷ (1)2
- Fe = [8.98 × 20 × 15 × 10-3] ÷ 1
- Fe = 8.98 × 20 × 15 × 10-3
- Fe = 2.69 N
Therefore, the electric force acting between two charged objects is 2.69 N.
Problem #2
Determine the electric force acting between two charged plastic balls separated by a distance of 150 cm. The proportionality constant, k, is 8.98 × 109 N m2/C2. The charges of the balls are q1 = 16 µC and q2 = 8 µC.
Solution
Given data:
- Electric force acting between two charged plastic balls, Fe = ?
- Distance between the two charged plastic balls, r = 150 cm = 1.5 m
- Proportionality constant, k = 8.98 × 109 N m2/C2
- Quantity of charge on 1st plastic ball, q1 = 16 µC = 16 × 10-6 C
- Quantity of charge on 2nd plastic ball, q2 = 8 µC = 8 × 10-6 C
Applying the formula:
- Fe = k [q1 q2] ÷ r2
- Fe = [(8.98 × 109) × (16 × 10-6) × (8 × 10-6)] ÷ (1.5)2
- Fe = [8.98 × 16 × 8 × 10-3] ÷ 2.25
- Fe = 1.1494 ÷ 2.25
- Fe = 0.51 N
Therefore, the electric force acting between two charged plastic balls is 0.51 N.
Problem #3
Given two spheres with charges of 30 µC and 7 µC, placed 2.1 m apart, find the value of the electric force acting between them. The proportionality constant, k, is 8.98 × 109 N m2/C2.
Solution
Given data:
- Quantity of charge on sphere 1, q1 = 30 µC = 30 × 10-6 C
- Quantity of charge on sphere 2, q2 = 7 µC = 7 × 10-6 C
- Distance between the two charged spheres, r = 2.1 m
- Electric force acting between two charged spheres, Fe = ?
- Proportionality constant, k = 8.98 × 109 N m2/C2
Applying the formula:
- Fe = k [q1 q2] ÷ r2
- Fe = [(8.98 × 109) × (30 × 10-6) × (7 × 10-6)] ÷ (2.1)2
- Fe = [8.98 × 30 × 7 × 10-3] ÷ 4.41
- Fe = 1.8858 ÷ 4.41
- Fe = 0.42 N
Therefore, the electric force acting between two charged spheres is 0.42 N.
Problem #4
Calculate the magnitude of the electric force between two charged balloons, separated by a distance of 250 cm. The proportionality constant, k, is 8.98 × 109 N m2/C2. The charges of the balloons are q1 = -25 µC and q2 = 5 µC.
Solution
Given data:
- Electric force acting between two charged balloons, Fe = ?
- Distance between the two charged sphere, r = 250 cm = 2.5 m
- Proportionality constant, k = 8.98 × 109 N m2/C2
- Quantity of charge on balloon 1, q1 = -25 µC = -25 × 10-6 C
- Quantity of charge on balloon 2, q2 = 5 µC = 5 × 10-6 C
Applying the formula:
- Fe = k [q1 q2] ÷ r2
- Fe = [(8.98 × 109) × (-25 × 10-6) × (5 × 10-6)] ÷ (2.5)2
- Fe = [8.98 × (-25) × 5 × 10-3] ÷ 6.25
- Fe = (-1.1225) ÷ 4.41
- Fe = -0.25 N
- |Fe| = |-0.25| = 0.25 N
Therefore, the magnitude of electric force acting between the two charged balloons is 0.25 N.
Related
- Force equation
- Normal force equation
- Net force formula
- Applied force formula
- Magnetic force equation
- Centripetal force equation
- Centrifugal force equation
- Spring force equation
- Tension force formula
- Electric force equation
External links
- Electric Forces, Fields & Potential | Equation & Relationship – Study.com
- Physics Tutorial: Coulomb’s Law – The Physics Classroom
- 2.8 Electric Field: Concept of a Field Revisited – BCcampus Pressbooks
- Coulomb’s Law Calculator – Omni Calculator
- 18.3 Electric Field – Physics – OpenStax
- Electric force (article) | Electrostatics – Khan Academy
- Coulomb’s law – Wikipedia
- What is the equation for calculating the electrical force, Fe, between two charges? – Quora
- 18.3: Coulomb’s Law – Physics LibreTexts
- Electric forces – HyperPhysics Concepts
- Coulomb’s Law: Calculating the Electrostatic Force – StickMan Physics
- Electric Force: Definition, Equation & Examples – Vaia
- Electric Field: Concept of a Field Revisited | Physics – Lumen Learning
- Q: How does electrical force equation related to Coulomb’s Law? – CK-12 Foundation
- Electric Charge And Electric Force Study Guide – Inspirit VR
- Electric Force – Physics – Socratic
- How to Calculate Electrostatic Force – Sciencing
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