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Homework Help: Current flow

  1. Oct 17, 2015 #1


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    Sodium ion flows a through a cylindrical ion channel --> diameter = 0.85 um and is 5 um long.
    potential difference b/w the ends of the channel is 225 mV
    drift velocity = 0.015 m/s
    in a period of 1 ms, a total of 15*10^6 ions exit the channel

    a. total charge exiting the channel in 1 ms =?
    b. current in the ion channel=?
    i have been trying to find b.) but I think my values might be wrong... PLEASE HELP ME!

    2. Relevant equations
    I=qnAv=Q/change in time
    change in time = length/drift velocity

    so for a. using the formula for Q:
    V=l*PIr^2= (5 um)(PI)(4.25*10^-7)^2=2.8*10^-18
    plugging in this value to the equation of Q, I get:
    Q=2.4*10^-12 (acc to the solutions on the book, this is right)

    Now, my problem is b....
    in this part, I used I=Q/t
    i know t = length/velocity so i plug in giving me =(5 um)(0.015 m/s)
    so now that i have t, i just use the Q from a to solve for I and I get 7.2*10^-9.
    however, according to the solutions this is wrong. it is suppose to be 2.4*10^-9...
    I have a feeling my Q value for this question is wrong since it's asking for the current IN the ion channel and the Q-value i have is the total charge exiting the channel... so how do I find the Q IN the ion channel??
    please help me..!!
  2. jcsd
  3. Oct 17, 2015 #2


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    Staff: Mentor

    You were given the time interval over which the stated number of ions exited the channel. It was 1 ms. That's the timeframe that is important for figuring the current.

    The drift velocity and channel dimensions are related to the current density. The time for a given ion to traverse the channel is not so important when there are many, many ions in a cross-section of the channel.
  4. Oct 17, 2015 #3


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    Oh Thank you so much! I have never taken physics back in high school so this is all new to me. I was sort of confused on what it meant by "period of 1 ms" (I thought it was a typo for m/s... I have never seen millisecond used before haha) so thank you for explaining it! :)
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