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!

Homework Help: Magnetic Vector Potential and conductor

  1. Dec 12, 2013 #1
    1. The problem statement, all variables and given/known data
    Show that, inside a straight current-carrying conductor of radius R, the vector potential is:
    $$ \vec{A} = \frac{\mu_{0}I}{4\pi}(1-\frac{s^2}{R^2}) $$

    so that ##\vec{A}## is set equal to zero at s = R

    2. Relevant equations

    ## \vec{A} = \frac{\mu_{0}}{4\pi}\int\frac{\vec{I}}{|r'-r|} dl' ##

    3. The attempt at a solution

    I'm really having a hard time even setting it up.
  2. jcsd
  3. Dec 13, 2013 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    Start by drawing a picture of a current carrying wire with a significant radius.
    How does the current vary with radius?
  4. Dec 13, 2013 #3

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper

    Hint: cylindrical coordinates.
    Some people like to turn the line integral into an area integral too ... there are lots of approaches.
    For marking - it is usually best to use the method covered in class.
  5. Dec 14, 2013 #4


    User Avatar
    Science Advisor
    Gold Member
    2017 Award

    Another hint: The Biot-Savart Law is not very efficient in many problems. It's easier to use the local form of the (magnetostatic) Maxwell Equations:
    [tex]\vec{\nabla} \times \vec{B}=\mu_0 \vec{j}, \quad \vec{\nabla} \cdot \vec{B}=0.[/tex]
    The second equation ("no monopoles") is already solved by the introduction of the vector potential, cf.
    [tex]\vec{B}=\vec{\nabla} \times \vec{A}.[/tex]
    So, just take the appropriate derivatives (in cylindrical coordinates), and check that you get the right current density.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted