NEET Class neet Answered

How did this come?

Asked by izranaur2017 | 16 Sep, 2019, 08:47: PM

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, 03:19: PM

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