1. Not finding help here? Sign up for a free 30min 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!

Breakdown voltage and electric field

  1. Oct 10, 2013 #1
    1. The problem statement, all variables and given/known data
    Hey guys. I am looking for confirmation regarding my logic concerning a specific principle. If I have a conducting, charged sphere that has a breakdown field of [itex]E_{breakdown}[/itex], and I want to know what the radius of the sphere has to be set to in order to reduce the breakdown voltage by half, would the following logic be correct:

    [itex]V_{breakdown} ∝ 1/r[/itex] and therefore [itex](1/2)V_{breakdown} ∝ 1/(2r)[/itex]. Hence to half the breakdown voltage, the radius is doubled.

    [itex]dV=\vec{E}.\vec{dl}[/itex], where for the specific radius [itex]2r[/itex], dl ends up at the radius, hence halving the potential means that the field is also halved. Hence,
    [itex]\vec{E}_{breakdown}/(2r)^2=0.5\vec{E}_{breakdown}[/itex], and [itex]r=0.7071[/itex].

    Thanks in advance!
     
  2. jcsd
  3. Oct 10, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    Hmm. I'd have thought that doubling the radius would double the breakdown voltage so that ##V_b ∝ r## ; Bigger spheres allow greater potential before sparks fly.

    Here's my thoughts:

    For a spherical charged surface:

    ##E = k \frac{Q}{r^2}~~~~## and ##~~~~ V = k \frac{Q}{r}##

    yieding V = Er

    Assuming that it's the field strength that's responsible for breakdown, for a given breakdown field strength ##E_b##, the corresponding breakdown voltage is

    ##V_b = E_b r##

    So to halve the breakdown voltage, halve the radius. Does that make sense?
     
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: Breakdown voltage and electric field
  1. Breakdown voltage (Replies: 11)

  2. Breakdown voltage (Replies: 2)

  3. Electric Field (Replies: 1)

Loading...