1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Confused how to use calculus in physics

  1. Sep 8, 2013 #1
    I understand simple concepts, like [itex]\frac{dx}{dt}=v[/itex] and why that is, but when I'm doing, for example, uniform charge distributions, I don't understand what the integral is actually doing. For example:

    [tex]E_x=∫dEcosθ[/tex]

    From what I learned in calculus, the dE means with respect to. So when taking an integral you usually have the form [tex]∫y(x)dx[/tex] and the interval is [a,b], which are x values.

    Why isn't the integral above in that form then? I mean at the very least, [itex]∫dθcosθ[/itex] would make more sense to me.
     
  2. jcsd
  3. Sep 8, 2013 #2
    Why isn't it in that form? Because you haven't made it into that form yet, that is your goal. You need to express E in terms of theta, or theta in terms of E, by looking at the geometry of the situation.

    Every little point in a charge distribution contributes to the overall electric field. If you just had 2 point charges you would add the fields in accordance with superposition. But now that you have an infinite number of points in a larger distribution, you need to do an integral to add them all up.
     
  4. Sep 10, 2013 #3
    Jd0g33,

    ∫ means a "sum" over differential amounts.

    In ∫dE cosθ the differential amount is dE cosθ

    dE is a vector and dE x cosθ is its projection on the x-axis.

    Adding up all the projections of every dE, you get E[itex]_{x}[/itex].

    When taking ∫y(x)dx, the differential amount being added up is y(x)dx, that is, y(x) times dx.
    This is the "area" under the point y(x).

    In this explanation, I have used some loose terms, but I hope I could pass the message.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook