Coulomb’s Law In Vector Form

Let the position vectors of charges q₁ and q₂ be r₁ and r₂ respectively Fig. We denote force on q₁ due to q₂ by F12 and force on q₂ due to q₁ by F21. The two point charges q₁ and q₂ have been numbered 1 and 2 for convenience and the vector leading from 1 to 2 is denoted by r₂₁:

 r₂₁ = r₂ – r₁.  In the same way, the vector leading from 2 to 1 is denoted by r₁₂: r₁₂ = r₁ – r₂ = – r₂₁ .The magnitude of the vectors r₂₁ and r₁₂ is denoted by r₂₁ and r₁₂, respectively (r₁₂ = r₂₁). The direction of a vector is specified by a unit vector along the vector. To denote the direction from 1 to 2 (or from 2 to 1), we define the unit vectors:

Coulomb’s force law between two point charges q₁ and q₂ located at r₁ and r₂ is then expressed as

If q­₁ and q₂ are of the same sign (either both positive and both negative), F₂₁ is along ˆr ₂₁, which denotes repulsion, as it should be for like charges. If q₁ and q₂ are of opposite signs, F21 is along – ˆr ₂₁(= ˆr ₁₂), which denotes attraction, as expected for unlike charges.

Thus, we do not have to write separate equations for the cases of like and unlike charges.  The force F12 on charge q₁ due to charge q₂, is obtained from force F21, by simply interchanging 1 and 2, i.e.

Thus, Coulomb’s law agrees with the Newton’s third law.

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Some of these questions which may be asked in your Board Examination 2012-2013

Q1: When a plastic comb is passed through dry hair, what type of charge is acquire by comb?

Q2: Does motion of a body affect its charge?

Q3: What is the origin of frictional forces?

Answer these questions in comment box and help your friends