Register to reply

Electric field in the overlap of two solid, uniformly charged spheres

by KaiserBrandon
Tags: electromagnetism, gauss law, sphere, uniform charge
Share this thread:
Oct6-10, 07:30 PM
P: 54
1. The problem statement, all variables and given/known data
Two spheres, each of radius R and carrying uniform charge densities +[tex]\rho[/tex]
and [tex]-\rho[/tex], respectively, are placed so that they partially overlap.
Call the vector from the positive centre to the negative centre [tex]\vec{d}[/tex]. Show
that the field in the region of overlap is constant and find its value. Use
Gaussís law to find the electric field inside a uniformly charged sphere

2. Relevant equations
law of superposition
Gauss Law

3. The attempt at a solution
I found the field inside one sphere to be
in the radial direction. Now for the overlapping spheres, I said that the vector from the centre of the positive sphere to some point P in the interlapping area is [tex]\vec{r}[/tex]. And from P to the centre of the negative sphere, I denoted [tex]\vec{r'}[/tex]. so [tex]\vec{r'}=\vec{d}-\vec{r}[/tex]. So in order for P to be inside the spheres, [tex]|\vec{r}|<R[/tex] and [tex]|\vec{d}-\vec{r}|<R[/tex]. So using the law of superposition, inside the overlap, the electric is
[tex]E = (|\vec{r}|-|\vec{d}-\vec{r}|)\rho/3\epsilon[/tex]
in the radial direction, with the boundaries in effect. Now I am stumped here, as I'm unsure how to reduce this to a constant. Any suggestions?
Phys.Org News Partner Science news on
'Smart material' chin strap harvests energy from chewing
King Richard III died painfully on battlefield
Capturing ancient Maya sites from both a rat's and a 'bat's eye view'
Oct6-10, 09:46 PM
P: 2,258
the electric field is a vector so why on earth are you reducing r and d-r to scalars?
Oct7-10, 12:23 PM
P: 54
yep, realized my mistake while sitting in my thermodynamics class this morning. It's funny how I usually figure stuff out while I'm not actually trying to do the question.

Oct7-10, 01:45 PM
P: 54
Electric field in the overlap of two solid, uniformly charged spheres

k, so I changed the E function to Cartesian coordinates. So in the overlap I got:


where d is the magnitude of [tex]\vec{d}[/tex]

And this is under the condition that [tex]\vec{d}[/tex] runs along the x axis.
Oct7-10, 06:57 PM
P: 2,258
sometimes you just need to sleep on it and get a fresh perpective on it in the morning

Register to reply

Related Discussions
Electric field inside a uniformly charged solid sphere . Introductory Physics Homework 1
Electric Field of a Uniformly Charged Ring Advanced Physics Homework 3
Electric Field of a Uniformly Charged Ring Introductory Physics Homework 3
Electric field due to a uniformly charged rod Introductory Physics Homework 1
Electric field at tip of uniformly charged cone Advanced Physics Homework 4