What Is the Electric Field in the Overlapping Region of Two Charged Spheres?

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SUMMARY

The discussion centers on calculating the electric field in the overlapping region of two charged spheres, one with a uniform positive charge density (+ρ) and the other with a uniform negative charge density (-ρ). Using Gauss' law, the electric field (E) from the positively charged sphere is derived as E = (ρr)/(3ε₀), while the electric field from the negatively charged sphere is equal in magnitude but opposite in direction. In the overlapping region, the fields from both spheres do not cancel each other out; instead, they combine to create a constant electric field directed from the positive to the negative sphere.

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Homework Statement


Two spheres, each radius R and carrying uniform charge densities +rho and -rho are placed so that they partially overlap. Call the vector from the positive center to the negative center dhat. Show that the field in the region of overlap is constant and find its value.

Homework Equations


Gauss' law.

The Attempt at a Solution


So I did Gauss' law for one sphere to find e-field. What I got was

E=(rho*r)/(3*episolon)

So the e-field from the positive sphere is E=(rho*r)/(3*episolon)
e-field from negative is the opposite of course.

principle of super position, don't they add up to zero?
 
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th5418 said:
So the e-field from the positive sphere is E=(rho*r)/(3*episolon)
e-field from negative is the opposite of course.
What direction does the field from each sphere point? In the area of overlap, do the fields point in opposite directions?
 

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