The **electric force equation**, based on Coulomb’s law, allows us to calculate the force between two charged objects. It is expressed as F_{e} = k [q_{1} q_{2}] ÷ r^{2}, where F_{e} represents the electric force, k is the Coulomb’s constant, q_{1} and q_{2} 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 × 10^{9} N m^{2}/C^{2}.

**Solution**

Given data:

- Electric force acting between two charged objects, F
_{e}= ? - Quantity of charge on object 1, q
_{1}= 20 µC = 20 × 10^{-6}C - Quantity of charge on object 2, q
_{2}= 15 µC = 15 × 10^{-6}C - Distance between the two charged objects, r = 1 m
- Proportionality constant, k = 8.98 × 10
^{9}N m^{2}/C^{2}

Applying the formula:

- F
_{e}= k [q_{1}q_{2}] ÷ r^{2} - F
_{e}= [(8.98 × 10^{9}) × (20 × 10^{-6}) × (15 × 10^{-6})] ÷ (1)^{2} - F
_{e}= [8.98 × 20 × 15 × 10^{-3}] ÷ 1 - F
_{e}= 8.98 × 20 × 15 × 10^{-3} - F
_{e}= 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 × 10^{9} N m^{2}/C^{2}. The charges of the balls are q_{1} = 16 µC and q_{2} = 8 µC.

**Solution**

Given data:

- Electric force acting between two charged plastic balls, F
_{e}= ? - Distance between the two charged plastic balls, r = 150 cm = 1.5 m
- Proportionality constant, k = 8.98 × 10
^{9}N m^{2}/C^{2} - Quantity of charge on 1
^{st}plastic ball, q_{1}= 16 µC = 16 × 10^{-6}C - Quantity of charge on 2
^{nd}plastic ball, q_{2}= 8 µC = 8 × 10^{-6}C

Applying the formula:

- F
_{e}= k [q_{1}q_{2}] ÷ r^{2} - F
_{e}= [(8.98 × 10^{9}) × (16 × 10^{-6}) × (8 × 10^{-6})] ÷ (1.5)^{2} - F
_{e}= [8.98 × 16 × 8 × 10^{-3}] ÷ 2.25 - F
_{e}= 1.1494 ÷ 2.25 - F
_{e}= 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 × 10^{9} N m^{2}/C^{2}.

**Solution**

Given data:

- Quantity of charge on sphere 1, q
_{1}= 30 µC = 30 × 10^{-6}C - Quantity of charge on sphere 2, q
_{2}= 7 µC = 7 × 10^{-6}C - Distance between the two charged spheres, r = 2.1 m
- Electric force acting between two charged spheres, F
_{e}= ? - Proportionality constant, k = 8.98 × 10
^{9}N m^{2}/C^{2}

Applying the formula:

- F
_{e}= k [q_{1}q_{2}] ÷ r^{2} - F
_{e}= [(8.98 × 10^{9}) × (30 × 10^{-6}) × (7 × 10^{-6})] ÷ (2.1)^{2} - F
_{e}= [8.98 × 30 × 7 × 10^{-3}] ÷ 4.41 - F
_{e}= 1.8858 ÷ 4.41 - F
_{e}= 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 × 10^{9} N m^{2}/C^{2}. The charges of the balloons are q_{1} = -25 µC and q_{2} = 5 µC.

**Solution**

Given data:

- Electric force acting between two charged balloons, F
_{e}= ? - Distance between the two charged sphere, r = 250 cm = 2.5 m
- Proportionality constant, k = 8.98 × 10
^{9}N m^{2}/C^{2} - Quantity of charge on balloon 1, q
_{1}= -25 µC = -25 × 10^{-6}C - Quantity of charge on balloon 2, q
_{2}= 5 µC = 5 × 10^{-6}C

Applying the formula:

- F
_{e}= k [q_{1}q_{2}] ÷ r^{2} - F
_{e}= [(8.98 × 10^{9}) × (-25 × 10^{-6}) × (5 × 10^{-6})] ÷ (2.5)^{2} - F
_{e}= [8.98 × (-25) × 5 × 10^{-3}] ÷ 6.25 - F
_{e}= (-1.1225) ÷ 4.41 - F
_{e}= -0.25 N - |F
_{e}| = |-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

Deep

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