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!

Electric field with electric potential

  1. May 1, 2016 #1
    1. The problem statement, all variables and given/known data
    A metallic hollow cylinder has a diameter of ##4.2 cm##. Along his axis there is a wire having a diameter of ##2.68 \mu m##(considering it as a hollow cylinder). Between the cylinder and the wire there is a voltage of ##855 V##.
    What is the electric field on the wire surface and the cylinder surface?

    2. Relevant equations
    Electric potential:
    ##\int_{A}^{B} \vec E_0 \cdot d\vec l = V_0(A) - V_0(B)##
    For a generic point ##P##
    ##V_0(x, y, z) = \int_A^P \vec E_0 \cdot d\vec l + V_0(A)##

    3. The attempt at a solution
    First I got the radius from the diameters, so:
    ##D_1 = 2.68\mu m = 2.68 * 10^-6 m##
    ##D_2 = 4.2 cm = 4.2 * 10^-2 m##
    ##R_1 = 1.34 * 10^-6 m##
    ##R_2 = 2.1 * 10^-2 m##

    At this point I know that ##V_0(R_1) - V_0(R_2) = 855 V##, so I have to use the first equation to find out ##E_0##. The problem is that I don't understand what ##E_0## I am calculating with this equation:
    $$\int_{R_1}^{R_2} \vec E_0 \cdot d\vec l = V_0(R_1) - V_0(R_2)$$
    Is it the wire surface? Or am I calculating the electric field inside the cylinder but outside the wire?
     
  2. jcsd
  3. May 1, 2016 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    You could try the differential form: ##\vec E=-\vec \nabla V## and select a suitable coordinate system and boundary conditions.
     
  4. May 2, 2016 #3
    Boundary conditions? What do you mean by that?
     
  5. May 2, 2016 #4

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Where is that equation from? You should use only such formulas which are explained.
    You certainly know that the line integral between two points does not depend on the path taken and ##\int_{A}^{B} \vec E \cdot d\vec l = V(A) - V(B)## where the integral goes along the radius now, from the wire surface to the surface of the cylinder. You have to know how the electric field depends on the radius. For that, use Gauss' Law.
     
  6. May 2, 2016 #5

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    Boundary conditions are the conditions on the boundary of the problem. Your problem has two boundaries - which is the cylinder surfaces.
    The relevant condition on those boundaries is the potentials there.
    Do you not know how to solve differential equations?

    Do you know how to use cylindrical-polar coordinates?
    Do you know Gauss' Law?
     
  7. May 3, 2016 #6
    Differential equations are those where you derive for each unknown and take the others as constant. (x, y, z in this case, since we have three coordinates)
    I never used the cylindrical and polar coordinates but I read about them in the book.
    Yes, I know the Gauss' Theorem.

    But how? I don't know the charge distribution.
     
  8. May 3, 2016 #7

    ehild

    User Avatar
    Homework Helper
    Gold Member

    But you know the symmetry of the problem. You can assume that the charge distribution is even, the charge is λ on unit length of the wire.
    And you know the potential difference between the metallic surfaces. The metallic surfaces are equipotentials, and the electric field is perpendicular to them, and is the same in every direction. The blue lines show the electric field lines, and the grin circle is the cross section of a Gaussian cylinder. Apply Gauss Law to get the electric field intensity at distance r from the axis.
    upload_2016-5-3_17-53-13.png
     
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: Electric field with electric potential
Loading...