# Electric force

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Electric force is the force of attraction or repulsion between charged particles due to their electric fields. It is one of the fundamental forces of nature and is described by Coulomb’s law, which states that the force between two charges is directly proportional to the product of their magnitudes and inversely proportional to the square of the distance between them. For instance, when you rub a balloon on your hair, electrons transfer from your hair to the balloon, creating a static electric charge. This charge allows the balloon to stick to a wall because of the electric force between the charged balloon and the neutral wall. Electric force is crucial in a wide range of phenomena, from the behavior of atoms and molecules to the operation of electrical devices and the transmission of electrical power.

Contents

## 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.