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Static Electricity Formula

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  • Last Updated : 25 Jun, 2022

Static electricity is defined as an imbalance of electric charges in a body, especially the negative and positive charges. In other words, the discharge of an electrical pulse is known as static electricity. Physical techniques are used to create the charge imbalance. Contact between solid things is one of the most prominent sources of static electricity. The static electricity generates a force during its creation which is directly proportional to the charges of both the bodies in contact and inversely proportional to the square of the distance between them. It is known as electrostatic force and is denoted by the symbol F. Its standard unit of measurement is Newtons (N), and the dimensional formula is given by [M1L1T-2].

Static Electricity Formula

F = 1/4πε0 (q1q2 / r2)

Where,

  • F is the electrostatic force,
  • 1/4πε0 = k0 is the Coulomb’s constant with a value of 9 × 109 Nm2C-2,
  • q1, q2 are the charge values,
  • r is the distance between the bodies.

Derivation

Consider a system of two bodies of charges q1 and q2 such that they are separated by a distance r. It is known that the static electricity force between these two bodies is directly proportional to the product of the charges of the bodies.

F ∝ q1q2 ⇢ (1)

Also, the force is indirectly proportional to the square of the distance between the two bodies. So we get,

F ∝ 1/r2 ⇢ (2)

From (1) and (2),

F ∝ q1q2/r2

Replacing the proportionality sign with a constant, we get,

F = k0q1q2/r2

Here, k0 is known as the Coulomb’s constant.

This derives the formula for static electricity force between two charged bodies.

Sample Problems

Problem 1: Calculate the static electricity force between two bodies of charge, 0.2 C and 0.4 C, separated by a distance of 0.1 m.

Solution:

We have,

q1 = 0.2

q2 = 0.4

r = 0.1

Using the formula we have,

F = 1/4πε0 (q1q2 / r2)

= (9 × 109 × 0.2 × 0.4)/0.01

= 2.87 × 109 N

Problem 2: Calculate the static electricity force between two bodies of charge, 1.5 C and 4 C, separated by a distance of 0.1 m.

Solution:

We have,

q1 = 1.5

q2 = 4

r = 0.1

Using the formula we have,

F = (9 × 109 × 1.5 × 4)/0.01

= 215.7 × 109 N

Problem 3: Calculate the static electricity force between two bodies of charge, 2 C and 3 C, separated by a distance of 1 m.

Solution:

We have,

q1 = 2

q2 = 3

r = 1

Using the formula we have,

F = (9 × 109 × 2 × 3)/1

= 53.92 × 109 N

Problem 4: Calculate the static electricity force between two bodies of charge, 4 C and 6 C, separated by a distance of 8 m.

Solution:

We have,

q1 = 4

q2 = 6

r = 8

Using the formula we have,

F = (9 × 109 × 4 × 6)/64

= 3.37 × 109 N

Problem 5: Calculate the static electricity force between two bodies of charge, 10 C and 3 C, separated by a distance of 2 m.

Solution:

We have,

q1 = 10

q2 = 3

r = 2

Using the formula we have,

F = (9 × 109 × 10 × 3)/4

= 67.4 × 109 N

Problem 6: Calculate the static electricity force between two bodies of charge, 3 C and 7 C, separated by a distance of 4 m.

Solution:

We have,

q1 = 3

q2 = 7

r = 4

Using the formula we have,

F = (9 × 109 × 3 × 7)/16

= 11.79 × 109 N

Problem 7: Calculate the static electricity force between two bodies of charge, 4 C and 9 C, separated by a distance of 12 m.

Solution:

We have,

q1 = 4

q2 = 9

r = 12

Using the formula we have,

F = (9 × 109 × 4 × 9)/144

= 2.24 × 109 N

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