Coulomb’s Law Equation | Problems (And Solutions)

Coulomb's Law Equation

Coulomb’s law equation states that the electric force (F) between two charged objects directly depends upon the quantity of their charges (q1 and q2) and inversely depends upon the square of distance (r) between them. Here’s the equation of coulomb’s law: F = k [q1 q2] ÷ r2

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 × 109 N m2/C2)

Solution:

Given data:
Electric force acting between two charged balls, F = ?
Quantity of charge on ball 1, q1 = 12 µC = 12 × 10-6 C
Quantity of charge on ball 2, q2 = 16 µC = 16 × 10-6 C
Distance between the two charged balls, r = 1 m
Coulomb’s constant, k = 8.98 × 109 N m2/C2

Using the equation of coulomb’s law,
F = k [q1 q2] ÷ r2
F = [(8.98 × 109) × (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 × 109 N m2/C2.

Solution:

Given data:
Quantity of charge on sphere 1, q1 = 25 µC = 25 × 10-6 C
Quantity of charge on sphere 2, q2 = 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 × 109 N m2/C2

Using the equation of coulomb’s law,
F = k [q1 q2] ÷ r2
F = [(8.98 × 109) × (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 q1 = 3 µC, q2 = 9 µC are separated by a distance of 2 m. If the value of coulomb’s constant is k = 8.98 × 109 N m2/C2, then calculate the value of electric force acting between these two charged objects.

Solution:

Given data:
Quantity of charge on an object 1, q1 = 3 µC = 3 × 10-6 C
Quantity of charge on an object 2, q2 = 9 µC = 9 × 10-6 C
Distance between the two charged objects, r = 2 m
Coulomb’s constant, k = 8.98 × 109 N m2/C2
Electric force acting between two charged objects, F = ?

Using the equation of coulomb’s law,
F = k [q1 q2] ÷ r2
F = [(8.98 × 109) × (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 q1 = 14 µC and q2 = 20 µC. (Take the value of coulomb’s constant, k = 8.98 × 109 N m2/C2)

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, q1 = 14 µC = 14 × 10-6 C
Quantity of charge on balloon 2, q2 = 20 µC = 20 × 10-6 C
Coulomb’s constant, k = 8.98 × 109 N m2/C2

Using the equation of coulomb’s law,
F = k [q1 q2] ÷ r2
F = [(8.98 × 109) × (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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