
Physics Physics Forum 
 LinkBack  Thread Tools  Display Modes 
December 18th, 2014, 02:54 AM  #1 
Senior Member Joined: Aug 2014 From: India Posts: 343 Thanks: 1  Is the charge distribution for an electric field unique?
If the electric field and boundary conditions are known exactly for a region of space, is it true that there exists only one charge distribution in that region of space that could have produced it? My understanding of the uniqueness theorem in electrostatics is that for a given charge distribution and boundary conditions for a volume, there exists only one (unique) solution to Poisson's equation, and thus the electric field in that volume is uniquely determined. Does the arrow point the other way, too? If we know the field and boundary conditions, is the charge distribution uniquely determined in the volume? Is there a simple example that illustrates why or why not? 
December 18th, 2014, 05:56 AM  #2 
Senior Member Joined: Apr 2014 From: Glasgow Posts: 2,134 Thanks: 720 Math Focus: Physics, mathematical modelling, numerical and computational solutions 
I'm not sure, but I think you are right. Comparing different charge distributions with equivalent electric fields boils down to considering purely radial systems, such as the charge sphere or the point charge. It is possible to show that a point charge has exactly the same electric field as a uniform charge density sphere with the same overall charge (fun task; this is true also with gravitational fields for spherical masses). However, this equivalence is only true outside the sphere; inside the sphere the charge differs from that of a point particle.


Tags 
charge, distribution, electric, field, unique 
Search tags for this page 
Click on a term to search for related topics.

Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
a little help with electric field lines  ibungo  Calculus  3  March 4th, 2013 08:16 PM 
Charge in a magnetic field and a electrostatic problem  Raphael  Physics  0  May 1st, 2012 01:23 PM 
How can a changing magnetic field induce an electric current  rsoy  Physics  1  March 7th, 2011 10:14 AM 
elementary electric field.  supermikong  Calculus  0  August 16th, 2010 12:40 AM 
Electric Field  johnny  Physics  2  May 1st, 2008 02:48 PM 