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!

Potential of the droplet.

  1. Dec 10, 2015 #1
    1. The problem statement, all variables and given/known data
    A conducting bubble of radius a, thickness t(t<<a) has potential V. Now the bubble collapses into a droplet. Find the potential of the droplet.


    2. Relevant equations
    Potential at the surface of bubble=##V##=##\frac{Kq}{a}##

    3. The attempt at a solution
    Potential at the surface of bubble=##V##=##\frac{Kq}{a}##
    bubble collapses into droplet.Let the radius of droplet to be R. Volume of droplet should be same as of bubble.
    volume of droplet=##\frac{4}{3}####πR^3##
    volume of bubble =##\frac{4}{3}####πa^3##
    ##\frac{4}{3}####πR^3##=##\frac{4}{3}####πa^3##
    Am I right till here?I don't think so,because I have not used thickness t anywhere.
     
  2. jcsd
  3. Dec 10, 2015 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    No. The bubble is a shell of thickness t. Its volume is not the same as the volume of the enclosed sphere.
     
  4. Dec 10, 2015 #3
    Volume of bubble=##(4πa^2)t ##?
     
  5. Dec 10, 2015 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Yes, when t<<a and a is the radius of the bubble.
     
  6. Dec 10, 2015 #5
    I have just guessed it !Is formula of volume of a shell is (4πradius squared)multiplied by thickness?
     
  7. Dec 10, 2015 #6

    NascentOxygen

    User Avatar

    Staff: Mentor

    To calculate the exact volume of material comprising the bubble wall, you would use "outer sphere's volume minus inner sphere's volume".
     
  8. Dec 10, 2015 #7
    Whenever thickness <<radius ,I should apply the below formula
    (4πradius squared)multiplied by thickness?
    And in case of droplet as nothing such is mentioned we will take as usual formula of volume 4/3 πr^3,right?
     
  9. Dec 10, 2015 #8

    NascentOxygen

    User Avatar

    Staff: Mentor

    That sounds like a good way to approximate it.
     
  10. Dec 10, 2015 #9
    Is my post #7correct?
     
  11. Dec 10, 2015 #10
    ##\frac{4}{3}####πR^3##=##(4πa^2)####t##

    ##R^3##=##3a^2####t##

    ##R##=(##3a^2####t##)^1/3 .................... . hope I have written it correctly

    potential of bubble=V(has been given)

    potential of droplet =V'(have to find)

    = ##\frac{V'}{V}##=##\frac{Kq}{R}## ÷ ##\frac{Kq}{a}##


    = ##\frac{Kq}{(3a^2t)^1/3}## ÷ ##\frac{Kq}{a}##

    = ##\frac{a}{(3a^2t)^1/3}##

    I don't know how to cancel these two
     
  12. Dec 10, 2015 #11

    ehild

    User Avatar
    Homework Helper
    Gold Member

    What do you want to cancel? You can simplify. Expand the power of 1/3
     
  13. Dec 10, 2015 #12
    Yes.I don't know how to do that
     
  14. Dec 10, 2015 #13

    ehild

    User Avatar
    Homework Helper
    Gold Member

    expand the denominator
     
  15. Dec 10, 2015 #14
    That is my problem.I don't know how to expand the denominator.Because numerator is only "a "we are not going to do anything with it.
    Can not we cancel "a "

    ##\frac{a}{(3a^2t)^1/3}##=##\frac{1}{(3at)^1/3}##
     
  16. Dec 10, 2015 #15

    Mister T

    User Avatar
    Science Advisor

    ##(a^2)^{\frac{1}{3}}=(a)^{\frac{2}{3}}##
     
  17. Dec 10, 2015 #16
    Why Can't we cancel "a see post #14
     
  18. Dec 10, 2015 #17

    ehild

    User Avatar
    Homework Helper
    Gold Member

    You do not cancel a. It stays in the formula. Post #14 is wrong. How do you rise a product to a power? How do you divide powers of a?
     
  19. Dec 10, 2015 #18

    Mister T

    User Avatar
    Science Advisor

    You cancel when ##\frac{a}{a}=1##. Not when ##\frac{a}{a^{2/3}}\neq 1##.

    Try, as an example, ##a=8##.
     
  20. Dec 10, 2015 #19
    ##\frac{a}{(3a^2t)^1/3}##=##\frac{a}{(3t)^1/3(a)^2\3}##
    Or if it is not clear
    L.png
     
  21. Dec 10, 2015 #20

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Simplify ##\frac{a}{a^{2/3}}##
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Potential of the droplet.
Loading...