Derive coulombs law in vector form_______.

Coulomb measured the force between two point charges and found that it varied inversly as the square of the distance between the charges and was directly proportional to the product of the magnitude of two charges and acted along the line of joining the two charges.

Thus if two point charges q_{1} and q_{2} are separated by a distance r in vacuum,

the magnitude of the force F between them is given by,

…(1)

The constant k in eqn.(1) is usually put as, so that Coulombs law is written as

…(2)

where εo is permitivity of free space and it is given by, εo = 8.854×10^{-12} C^{2}N^{-1}m^{-2}

Since force is vector, we need to write Coulombs law in vector notation.

vector quantity is given in Bold)

Let the position vectors of charges q_{1} and q_{2} be **r _{1}** and

**r**respectively. We denote force on q

_{2}_{1}due to q

_{2}by

**F**and

_{12}force on q_{2} by q_{1} by **F _{21}** as shown in figure. The two point charges q

_{1}and q

_{2}have been numbered 1 and 2 for conveneience

and the vector leading from 1 to 2 is denoted by **r _{21}**

**r _{21} = r_{2}-r_{1}** . The magnitude of vector

**r**is denoted by |

_{21}**r**|. The direction of a vector is specified by unit vector along that vector.

_{21}We define the unit vector

Coulombs force law between two point charges q_{1} and q_{2} located at **r _{1}** and

**r**is then expressed as

_{2}The above equation is valid for any sign of q_{1} and q_{2}. If q_{1} and q_{2} are of same sign, **F _{21}** is along

**r**, which denotes repulsion.

_{21}If they are opposite sign, **F _{21}** is along

**-r**that denotes attraction. No need to write separate equation for like and unlike charges

_{21}