# A problem of approximation [duplicate]

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?

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Possible duplicate: physics.stackexchange.com/q/21051/2451 –  Qmechanic Aug 14 '12 at 16:29

## marked as duplicate by Qmechanic♦, Manishearth♦Dec 10 '12 at 9:40

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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So you see, the assumption in classical electrodynamics that charge is a continuous variable is just an approximation, just like assuming the cannonball is a sphere. We all know that charges come in quanta of $e$, but if we're measuring a charge of 10 Coulombs - well, who cares about the electrons?