DI/dt depending on v?

[LaurieAG]

What differential are you referring to?I do not understand what you say.OK,you answer to this question.Can we define the electrostatic potwential if the test charge moves at velocity 1/3rd or 1/5th of c?

 

I was talking about the pure maths principles you are referring to. In calculus you differentiate a function with regards to one of the variables i.e. dI/dt is the differential of I with regards to t. Differentiation involves the application of n*x^(n-1) across a function for equations in the form of a*x^2 + b*x + c = 0 (where x is the variable and a, b & c are constants and can equal zero). Intergration is just the opposite of differentiation.

 

Plotting points along an x,y axis of the function gives us a line and the area under the curve (within a series of limits, and the x axis) is equivalent to the differential of the function and so on. (it could also be the area of the differential of your function between your specified limits (the integral), I'm a bit rusty)

 

In your example the answer is the areas under the curve with the slower velocities having longer limits (on the x axis, time) while faster velocities will have shorter limits.