**Electric force **(F_{e}) is defined by the coulomb’s law. Using the equation of electric force: **F**_{e}** = k [q**_{1}** q**_{2}**] ÷ r**** ^{2}**, the value of electric force acting between two charged objects can be calculated.

Let’s solve some problems based on this equation, so you’ll get a clear idea.

## Electric Force Practice Problems

**Problem 1:** Two objects 1 and 2 with charges 20 µC and 15 µC are separated by a distance of 1 m. Calculate the value of electric force acting between these two charged objects. (Take the value of proportionality constant, k = 8.98 × 10^{9} N m^{2}/C^{2})

Solution:

Given data:

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}

Electric force acting between two charged objects, F_{e} = ?

Using the equation of electric force,

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:** Find the value of electric force acting between the two charged plastic balls which are separated by a distance of 150 cm, if the value of proportionality constant k = 8.98 × 10^{9} N m^{2}/C^{2}, q_{1} = 16 µC and q_{2} = 8 µC.

Solution:

Given data:

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

Electric force acting between two charged plastic balls, F_{e} = ?

Using the equation of electric force,

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:** Two spheres with charges 30 µC and 7 µC are placed 2.1 m apart. If the value of proportionality constant k = 8.98 × 10^{9} N m^{2}/C^{2}, then what is the value of electric force acting between these two charged spheres?

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 sphere, r = 2.1 m

Proportionality constant, k = 8.98 × 10^{9} N m^{2}/C^{2}

Electric force acting between two charged spheres, F_{e} = ?

Using the equation of electric force,

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:** Find the magnitude of electric force acting between the two charged balloons which are separated by a distance of 250 cm, if the value of proportionality constant k = 8.98 × 10^{9} N m^{2}/C^{2}, q_{1} = -25 µC and q_{2} = 5 µC.

Solution:

Given data:

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

Distance between the two charged sphere, r = 250 cm = 2.5 m

Proportionality constant, k = 8.98 × 10^{9} N m^{2}/C^{2}

Electric force acting between two charged balloons, F_{e} = ?

Using the equation of electric force,

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**.

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**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

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