Sunday, March 13, 2016

electricity - A problem of approximation






Possible Duplicate:
Why are continuum fluid mechanics accurate when constituents are discrete objects of finite size?



When we apply differentiation on charge being conducted with respect to time,i.e dq/dt, we consider the charge flown to be infinitely small, but q cannot be less than 1.602*10^-19. So how can we assume this to be infinitely small?



Answer



Even a physical quantity which changes by discrete amounts can often be well approximated by a continuous function of time.


The derivative is a property of a mathematical function. Any differentiable function must necessarily be continuous, and a continuous function will change by arbitrarily small values for an arbitrarily small change in inputs.


The fact that one can calculate the derivative of a function does not imply that the physical quantity that is approximated by that function can also be changed by arbitrarily small amounts.


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