Coulomb’s Law

Coulomb’s Law-  It states that force between two point charges is directly proportional to the product of  the magnitude of two charges & inversely proportional to the square of distance between them . The direction of  force is along  the line joining two point charges.

  Mathematically,

                          F µ q₁ q₂/r²                   q₁·----------------------------------·q₂

                          F = k q₁ q₂/r^{2                         ______________   r    _________________}                         

Case 1-  When medium between two charges is air/vacuum/free space

                                                 k = 1/4Õe_o    

                     then                      F =  1/4Õe_o´ q₁ q₂/r²     (e_{o = 8×854 ´10}^-12 C²N^-1m^-2 )

Case 2-   When medium between two charges is other than air

                                                 k = 1/4Õe

                      Then                   F = 1/4Õe ´ q₁ q₂/r²      

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 QUESTION-  A charge q is placed at the centre of line joining two equal charges Q. Show that the system of three charges will be in equilibrium if q = -Q/4 ?

SOLUTION- Let two equal charges  Q each be held A and B , where AB = 2x & C is the centre of AB , where q is held         ^{______________   2x   _________________}                         

                                                        ·-----------------·-----------------·

                                                        A                     C                       B

                    

      Net force on q is zero, so q is already is in equilibrium

                         Now total charge on Q at B

                         1/4Õe _o´Qq/x² +  1/4Õe _o´QQ/(2x)² = 0

                                                           1/4Õe _o´Qq/x² =-1/4Õe _o´QQ/(2x)²

                                                                           So  q =  -Q/4   (HENCE PROVED)