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,
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ReplyDeleteall the solutions are great and have used good amount of calculus . by the way thanks , this is really helping me .
ReplyDeletewhy can`t we take our gaussian surface as sphere.. won`t that be much easier
ReplyDeleteE.f is not uniform so gauss approach will no wrk
DeleteWe don't take a sphere because we are asked to find the flux through a plane across the balls section.
Deletehow r°/r = cos theta
ReplyDeleteThat's what I was wondering.
Deleter is labelled incorrectly it is the radius of the dotted sphere I assume
DeleteThat's what I was wondering.
ReplyDelete