Coulomb’s Law

COULOMB’S LAW

The force of interaction of two stationary point charges in vacuum is directly proportional to the product of these charges and inversely proportional to the square of their separation

F = kq ₁ q ₂ /r ² (1.1)

where k is a constant which depends on the system of units. Its value in SI unit is

k = 9 × 109 Nm2C-2

The constant is often written in the form

k = 1/4πε ₀

where ε0 is called the permitivity constant  which is numerically equal to

εo = 8.85 × 10−12 C2 /Nm2

F ₁₂ =  (kq ₁ q ₂ /r2) r ₁₂ (1.2)

where r ₁₂ is the unit vector, directed from q1 to q2  and F ₁₂ is the force on the charge q1 due to q2. Similarly force on charge q2 due to q1 is F ₂₁ .

F ₂₁ =  (kq ₁ q ₂ /r2) (-r ₁₂ )

Important points regarding Coulomb’s law

1.Charges are assumed to be at rest.

When charges are in motion they also produce and experience magnetic forces.

Principle of Superposition

How to solve a problem using Coulomb’s law ?

1.Decide whether the force due to a given charge is attractive or repulsive and express it by drawing vectors.

2.Find the magnitude of the force using Coulomb’s law − ignoring the signs of the charges.

3.Resolve the forces along the given co−ordinate axes and express them in vector form using i, j ,k unit vector notation unless otherwise specified.

4.Use the principle of superposition to find the net force on a charge.

Example: 1.1

F12 = = 32 × 10−5 N

F13 = = 23 × 10−5 N

F14 = = 54 × 10−5 N

3. F12 = −(32 ×10−5)j

F13  = −(F13cosθ)i + (F13 sinθ)j =

= 10−5 [−18.4 i + 13.8 j]

F14  = −(54 × 10−5) i

4.The net force on q1 is

F1 = F12  + F13 + F14

F1 = 10−5 [−72.4i − 18.2j] N