**Coulomb’s law equation** states that the **electric force** (F) between two charged objects directly depends upon the **quantity of their charges** (q_{1} and q_{2}) and inversely depends upon the square of **distance **(r) between them. Here’s the equation of coulomb’s law: **F = k [q**_{1}** q**_{2}**] ÷ r**^{2}

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

## Coulomb’s Law Practice Problems

**Problem 1:** Calculate the electric force acting between the two balls 1 and 2 with charges 12 µC and 16 µC which are separated by a distance of 1 m. (Take the value of coulomb’s constant, k = 8.98 × 10^{9} N m^{2}/C^{2})

Solution:

Given data:

Electric force acting between two charged balls, F = ?

Quantity of charge on ball 1, q_{1} = 12 µC = 12 × 10^{-6} C

Quantity of charge on ball 2, q_{2} = 16 µC = 16 × 10^{-6} C

Distance between the two charged balls, r = 1 m

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

Using the equation of coulomb’s law,

F = k [q_{1} q_{2}] ÷ r^{2}

F = [(8.98 × 10^{9}) × (12 × 10^{-6}) × (16 × 10^{-6})] ÷ (1)^{2}

F = [8.98 × 12 × 16 × 10^{-3}] ÷ 1

F = 1724.16 × 10^{-3}

F = 1.72 N

Therefore, the electric force acting between two charged balls is **1.72 N**.

**Problem 2:** Two metal spheres with charges 25 µC and 6 µC are separated by a distance of 1.1 m. Calculate the value of electric force acting between these two charged spheres, if the value of coulomb’s constant is k = 8.98 × 10^{9} N m^{2}/C^{2}.

Solution:

Given data:

Quantity of charge on sphere 1, q_{1} = 25 µC = 25 × 10^{-6} C

Quantity of charge on sphere 2, q_{2} = 6 µC = 6 × 10^{-6} C

Distance between the two charged spheres, r = 1.1 m

Electric force acting between two charged spheres, F = ?

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

Using the equation of coulomb’s law,

F = k [q_{1} q_{2}] ÷ r^{2}

F = [(8.98 × 10^{9}) × (25 × 10^{-6}) × (6 × 10^{-6})] ÷ (1.1)^{2}

F = [8.98 × 25 × 6 × 10^{-3}] ÷ 1.21

F = 1113.22 × 10^{-3}

F = 1.11 N

Therefore, the electric force acting between two charged spheres is **1.11 N**.

**Problem 3:** Two charged objects with charges q_{1} = 3 µC, q_{2} = 9 µC are separated by a distance of 2 m. If the value of coulomb’s constant is k = 8.98 × 10^{9} N m^{2}/C^{2}, then calculate the value of electric force acting between these two charged objects.

Solution:

Given data:

Quantity of charge on an object 1, q_{1} = 3 µC = 3 × 10^{-6} C

Quantity of charge on an object 2, q_{2} = 9 µC = 9 × 10^{-6} C

Distance between the two charged objects, r = 2 m

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

Electric force acting between two charged objects, F = ?

Using the equation of coulomb’s law,

F = k [q_{1} q_{2}] ÷ r^{2}

F = [(8.98 × 10^{9}) × (3 × 10^{-6}) × (9 × 10^{-6})] ÷ (2)^{2}

F = [8.98 × 3 × 9 × 10^{-3}] ÷ 4

F = 60.615 × 10^{-3}

F = 6.06 × 10^{-2} N

Therefore, the electric force acting between two charged objects is **6.06 × 10 ^{-2} N**.

**Problem 4:** Calculate the value of electric force acting between the two charged balloons separated by a distance of 1.4 m. The value of charges on the balloons are q_{1} = 14 µC and q_{2} = 20 µC. (Take the value of coulomb’s constant, k = 8.98 × 10^{9} N m^{2}/C^{2})

Solution:

Given data:

Electric force acting between two charged balloons, F = ?

Distance between the two charged balloons, r = 1.4 m

Quantity of charge on balloon 1, q_{1} = 14 µC = 14 × 10^{-6} C

Quantity of charge on balloon 2, q_{2} = 20 µC = 20 × 10^{-6} C

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

Using the equation of coulomb’s law,

F = k [q_{1} q_{2}] ÷ r^{2}

F = [(8.98 × 10^{9}) × (14 × 10^{-6}) × (20 × 10^{-6})] ÷ (1.4)^{2}

F = [8.98 × 14 × 20 × 10^{-3}] ÷ 1.96

F = 1282.85 × 10^{-3}

F = 1.28 N

Therefore, the electric force acting between two charged balloons is **1.28 N**.

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