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

by KaiserBrandon
Tags: electromagnetism, gauss law, sphere, uniform charge
 P: 54 1. The problem statement, all variables and given/known data Two spheres, each of radius R and carrying uniform charge densities +$$\rho$$ and $$-\rho$$, respectively, are placed so that they partially overlap. Call the vector from the positive centre to the negative centre $$\vec{d}$$. Show that the field in the region of overlap is constant and find its value. Use Gauss’s law to find the electric field inside a uniformly charged sphere first. 2. Relevant equations law of superposition Gauss Law 3. The attempt at a solution I found the field inside one sphere to be $$(r\rho)/(3\epsilon)$$ 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 $$\vec{r}$$. And from P to the centre of the negative sphere, I denoted $$\vec{r'}$$. so $$\vec{r'}=\vec{d}-\vec{r}$$. So in order for P to be inside the spheres, $$|\vec{r}|  P: 2,258 the electric field is a vector so why on earth are you reducing r and d-r to scalars?  P: 54 yep, realized my mistake while sitting in my thermodynamics class this morning. It's funny how I usually figure stuff out while I'm not actually trying to do the question.  P: 54 Electric field in the overlap of two solid, uniformly charged spheres k, so I changed the E function to Cartesian coordinates. So in the overlap I got: [tex]\vec{E}=\frac{\rho*d}{3*\epsilon}*\hat{i}$$ where d is the magnitude of $$\vec{d}$$ And this is under the condition that $$\vec{d}$$ runs along the x axis.