WHILE DERIVING THE FORMULA FOR THE POTENTIAL ENERGY AT A POINT DUE TO POINT CHARGE

WE MULTIPLY THE FORCE ON THE TEST CHARGE DUE TO THE POINT CHARGE(AT THE INITIAL POSITION)WITH A SMALL DISTANCE dR AND THEN INTEGRATE IT TO FIND THE TOTAL POTENTIAL ENERGY.wHY DO WE TAKE THE SAME INITIAL FORCE ON THE PARTICLE WHEN WE KNOW THAT AT A DIFFERENT POSITION THE FORCE WILL BE DIFFERENT?(INFACT FORCE WILL DIFFER EVEN WITH A SMALL DISPLACEMENT)

Dear anshuman

force is not constant .

we are taking F=q1q2/4∏ε r

force is dependent on r

if we perform intigration then for different value of limit r is different and thus force is different.

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