My Math Forum  

Go Back   My Math Forum > Science Forums > Physics

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?
Ganesh Ujwal is offline  
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.
Benit13 is offline  

  My Math Forum > Science Forums > Physics

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 r-soy 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

Copyright © 2019 My Math Forum. All rights reserved.