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Asked by izranaur2017 | 16 Sep, 2019, 20:47: PM
answered-by-expert Expert Answer
F12 is the force acting on charge q1 due to charge q2, if the sign of charges are same.
Since force is vector quantity, we need to write Coulomb's law in vector form indicating the direction of force.
Direction of force F12 is the direction of line joining from q2 to q1, pointing towards q1.
Hence a unit vector along the direction of q2 to q1  i.e., begin mathsize 12px style stack r subscript 21 with hat on top space end style is given in the Coulomb's law
because begin mathsize 12px style stack r subscript 21 with rightwards arrow on top equals space stack r subscript 1 with rightwards arrow on top space minus space stack r subscript 2 with rightwards arrow on top space end style is vector pointing towards q1 and starting from q2.

F21 is the force acting on charge q2 due to charge q1, if the sign of charges are same.
Direction of force  F21 is direction of  line joining from q1 to q2, pointing towards q2.
Hence a unit vector along the direction of q1 to q2 i.e., begin mathsize 12px style stack r subscript 12 with hat on top space space end style is given in the Coulomb's law,
because begin mathsize 12px style stack r subscript 12 with rightwards arrow on top equals space stack r subscript 2 with rightwards arrow on top space minus space stack r subscript 1 with rightwards arrow on top space end style is vector pointing towards q2 and starting from q1.

unit vector  begin mathsize 12px style stack r subscript 21 with hat on top space equals space fraction numerator stack r subscript 1 with rightwards arrow on top space minus space stack r subscript 2 with rightwards arrow on top over denominator open vertical bar stack r subscript 1 with rightwards arrow on top space minus space stack r subscript 2 with rightwards arrow on top close vertical bar end fraction space end style  and  begin mathsize 12px style open vertical bar stack r subscript 1 with rightwards arrow on top space minus space stack r subscript 2 with rightwards arrow on top close vertical bar space equals space r end style,
we write coulomb's law as , begin mathsize 12px style stack F subscript 12 with rightwards arrow on top space equals space fraction numerator k space q subscript 1 q subscript 2 over denominator open vertical bar stack r subscript 1 with rightwards arrow on top space minus space stack r subscript 2 with rightwards arrow on top close vertical bar cubed end fraction space open parentheses stack r subscript 1 with rightwards arrow on top space minus space stack r subscript 2 with rightwards arrow on top close parentheses end style
 
Answered by Thiyagarajan K | 17 Sep, 2019, 15:19: PM

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