Sunday, March 28, 2010

Irodov Problem 3.21



The electric field at a distance r from the center of the sphere can be calculated using Gauss law easily as,



E will be directed along the radius vector.

From elementary geometry we can see that,



Hence,



The component of electric field along the z-axis is given by,


Equation (4) basically tells us that the component of electric field along the z-axis does not depend on in other words its same all over the disc section at a distance ro from the center.

The total area of the disc section is given by,





Since the area vector of the disc section is directed along the z-axis, the total flux through this disc section is given by,

6 comments:

  1. This comment has been removed by the author.

    ReplyDelete
  2. all the solutions are great and have used good amount of calculus . by the way thanks , this is really helping me .

    ReplyDelete
  3. why can`t we take our gaussian surface as sphere.. won`t that be much easier

    ReplyDelete
    Replies
    1. E.f is not uniform so gauss approach will no wrk

      Delete
    2. We don't take a sphere because we are asked to find the flux through a plane across the balls section.

      Delete