Write the complete explicit vector form of Coulomb's law.

Solution

Consider two charges q₁ and q₂. Let the position vectors of the respective charges be r₁ and r₂.

Let, the force acting on q₁due to q₂be F₁₂and the force acting on q₂due to q₁be F₂₁.

The vector leading from 1 to 2 is denoted by r_{21 :} r₂₁= r₂- r₁
$∥$ ly, vector leading from 2 to 1 is denoted by r₁₂:
r₁₂=r₁- r₂and
  r₁₂=-r_21.

The direction of a vector is specified by a unit vector along the vector.

   ${\overset{⏜}{r}}_{21} = - {\overset{⏜}{r}}_{12}$

Now, Coulomb's force law between two point charges q₁and q₂ when force is acting on q₂ due to q₁is expressed as:

$F_{21} = \frac{1}{4 {πε}_{\circ}} \frac{q_{1} q_{2}}{{r_{21}}^{2}} {\overset{⏜}{r}}_{21}$

And, force acting on q₁due to q₂can be expressed as:

$F_{12} = \frac{1}{4 {πε}_{\circ}} \frac{q_{1} q_{2}}{{r_{12}}^{2}} {\overset{⏜}{r}}_{12}$

$∴ F_{12} = - F_{21}$

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Electric Charges And Fields

Write the complete explicit vector form of Coulomb's law.

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Figure shows tracks of three charged particles in a uniform electrostatic field. Give the signs of the three charges. Which particle has the highest charge to mass ratio?

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