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

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The discussion focuses on determining the electric field in the overlapping region of two charged spheres with uniform charge densities of +rho and -rho. Using Gauss' law, the electric field from the positive sphere is calculated as E=(rho*r)/(3*epsilon), while the negative sphere produces an opposing field. The principle of superposition suggests that these fields should cancel each other out in the overlap region. However, the direction of the electric fields from each sphere must be considered, as they point in opposite directions. The conclusion emphasizes that the fields do not add up to zero in the overlapping area due to their opposing directions.
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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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