What does the notation dQ/dt mean in calculus and physics?

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In summary, the equation I = dQ/dt represents the instantaneous current in a conductor, with dQ and dt being infinitesimally small changes in charge and time, respectively. This notation is a calculus definition that is applicable in both physics and calculus, and dQ has a meaning that is dependent on the context in which it is used but can be thought of as a very small change in the variable Q.
  • #1
rambo5330
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I'm taking a calculus based physics class this year and I've had a few issues getting reliable information on the following notation


the following equation I = [tex]\frac{dQ}{dt}[/tex]

the previous equatin represents the instantaneous current in a conductor.

what exactly is the term dQ or dt saying. in calculus if i see [tex]\frac{dy}{dx}[/tex]

I know it means take the derivative of this with respect to x.
now from my understanding d is like delta but where as delta may deal with rather large changes etc d represents an infinitly small piece of something i.e. an infinitely small charge over and infinitely small time? is that what that is saying

and whatever meaning it does have is it related completely to calculus itself or is this a physics definition?

thank you...
 
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  • #2
The actual derivative (dy/dx) is just equal to the:

Limx-Inf f(x+delta x) - f(x)all over delta x

It is called the limit definition of the derivative, and it is a calculus definition that can be used both in physics and calculus. It isn't used in solely one or the other
 
  • #3
I understand that part, its the actual meaning of the symbol dQ... or dx for that matter that I am looking for

what I am finding so far is that dQ could mean an infinitly small portion of a larger charge Q
 
  • #4
Officially, dq is part of a larger complex and the meaning is given by the context. It doesn't have a meaning by itself. But I like to think of it as a really small change of the variable. You might think of dQ/dt as "the ratio of really small changes of Q and t".
 
  • #5


In calculus and physics, the notation dQ/dt represents the derivative of a quantity Q with respect to time, t. This can also be written as Q' or dQ/dt. It is a mathematical way of expressing the rate of change of a quantity with respect to time, which is a fundamental concept in both calculus and physics. In the context of your equation, dQ represents a small change in charge and dt represents a small change in time. Taking the derivative of this equation allows us to determine the rate of change of current (I) over time, which is a crucial concept in understanding the behavior of electrical circuits. This notation is used in both calculus and physics, as it is a fundamental concept that is relevant in both fields.
 

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Notation clarification is important because it helps to avoid confusion and misinterpretation of data. It ensures that all researchers are using the same notation and have a clear understanding of its meaning.

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