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Finding the force of repulsion between two point charges

  1. Apr 15, 2017 #1
    Hello! So this is going into physics because it is a physics problem, but it is maths that is the real problem. So if you came here to help someone with physics and not maths I'm sorry.

    1. The problem statement, all variables and given/known data


    Find the force of repulsion between two point charges of +1C and +3C if they are placed 1 m apart in a vacuum. On which charge is the greater force?

    So here is what I know

    ε=8.9x10-12
    π = 3.14
    d = 100 cm
    q1 = 1
    q2 = 3
    cats are soft and warm

    2. Relevant equations

    here is the formula I have to use

    F= 1/4πε0 Q1 Q2/d2

    I can't find pi on the thing. Is this supposed to be pi: π?It looks like a Russian L. This is hard enough without alternate fonts.

    3. The attempt at a solution

    This is going to be my fourth time trying this.

    The correct answer should be 2.682 x 1010

    Am I right in thinking that 10-2 x 10-2 =10-4? It's just 100 x 100 = 10,000, right?

    1 (1 x 10 -6) ( 3x 10-6)
    _______________________________________________
    4π(8.9 x 10-12)(100)

    Here's my attempt at solving what's above the line:

    3 x 10 -12
    ________________________________
    4π(8.9 x 10-12)(100)

    I'm less confident about what's below. Do I multiply pi by 4 first?

    3 x 10 -12
    ________________________________
    12.5(8.9 x 10-12)(100)

    Like that?

    Am I right in thinking that 8.9 x 10-12 x 100 = 8.9 x 10-14?

    So now I have

    3 x 10 -12
    ______________________________
    12.5 (8.9 x 10-14)


    3 x 10 -12
    ____________________________
    106.8 x 10-14)

    So there are 2 zeros there that I've put in bold that I think I have to get rid of, and I'm going to add them onto that little -14
    1.068 x 10-16. Is that right?


    3 x 10 -12
    ___________________________
    1.068 x 10-16

    Now there are loads of zeros above and below the line, am I right in thinking I can cross them out? the difference between -12 and -16 is 4, so I'll get rid of the -12 all together and leave -4 below.

    3 x 10
    _________________________
    1.068 x 10-4

    It occurs to me that 3 x 10 is 30 and that 1.068 x 10000 is 10680

    30
    ______
    10680

    = 0.00289575289 N

    Low and behold.. not the right answer. It is the second time I got this same answer though so at least that's something, I suppose.

    I'd really appreciate it if, even something that would inevitably cause me to get the wrong answer happened very early on, you'd tell me if there were other silly things I did with the numbers later.

    Thank you!
     
  2. jcsd
  3. Apr 15, 2017 #2
    Hi Rabbit:

    I think your problem may be with units. I suggest you rewrite each of your numeric equations and variable definitions, and include the corresponding units.

    Hope this helps.

    Regards,
    Buzz
     
  4. Apr 15, 2017 #3

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Yes.

    ##10^{-2}= \frac{1}{100}##. So, ##10^{-2} \times 10^{-2} = \frac{1}{100} \times \frac{1}{100} = \frac{1}{100 \times 100} = \frac{1}{10000} = 10^{-4}##

    The statement of the problem gives the charges as 1 C and 3 C, not 1 x 10-6 C and 3 x 10-6 C.

    Also, if you are using Coulombs for the charge, then you are working in the SI system of units. In this system of units, the unit of length is the meter, not the centimeter. So, you will need to convert 100 cm to meters.

    When you multiply several numbers together, it does not matter what order you multiply them. So, yes, you can multiply π by 4 first.

    No. Note that 100 = 102.
    So, 10-12 x 100 = 10-12 x 102 = 10-12+2 = 10-10.

    You are right that you want to add 2 to -14. But that doesn't give you -16.

    When you combine the -12 and -16 to get 4, you have used up all the factors of 10 in the numerator. So, your numerator becomes 3, not 3 x 10.
     
  5. Apr 18, 2017 #4
    cool

    Ah! Sorry, this was a big mistake. I was looking at the sample method, where they were using microunits
    This is confusstipating because in the sample the book has an example with 50 cm and uses 50 as d in the sample method, not 0.5.. But ok!


    cool :)
    Ah yes thank you. Was confusing -12 with 12
    doi *smacks head*
    Thank you! :) Thank you so much!
     
  6. Apr 18, 2017 #5
    1. The problem statement, all variables and given/known data

    Find the force of repulsion between two point charges of +1C and +3C if they are placed 1 m apart in a vacuum. On which charge is the greater force?

    ε=8.9x10-12
    π = 3.14
    d = 100 cm
    q1 = 1
    q2 = 3
    2. Relevant equations

    F= 1/4πε0 Q1 Q2/d2

    3. The attempt at a solution

    The correct answer should be 2.682 x 1010

    10-2 x 10-2 =10-4

    1 x 3
    _______________________________________________
    4π(8.9 x 10-12)(1)


    3
    _____________________________
    4π(8.9 x 10-12)(1)

    3
    _____________________________
    12.5(8.9 x 10-12)(1)

    3
    ___________________________
    111.25 x 10 -12)

    3
    ___________________
    1.125 x 10 -10)

    =2.67 -10N ............ X

    What am I doing wrong?

    So sorry, I did try twice before submitting, and I went over everything for a good 20 minutes.
     
  7. Apr 18, 2017 #6

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Everything is ok except for the very last step. You did not correctly treat the 10-10 in the denominator in arriving at your final answer.

    What is ##\frac{1}{10^{-10}}##?
     
    Last edited: Apr 18, 2017
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