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## Homework Statement

consider 2 uniform static electric charge densities +/-[tex]\rho[/tex] located in the volumes defined by the 2 intercepting spheres of radius a. Charges are located in free space and [tex]\rho[/tex][tex]\delta[/tex] is a constant c.

The center of the spheres are separated by distance [tex]\delta[/tex]

The upper sphere has charge density +[tex]\rho[/tex] and lower has -[tex]\rho[/tex]

Show that E(P) in the region belonging to both spheres is constant and given by -[tex]\hat{z}[/tex]c/3[tex]\epsilon[/tex]

_{0}

## Homework Equations

## The Attempt at a Solution

Charge Q= [tex]\rho[/tex](4/3pi a

^{3})

I tried for +ve charged sphere E(P) = (Q/(4pi[tex]\epsilon[/tex])R

^{3})[ 3

**R.d**/R

^{2}

**R-d**]

I was able to get

E(P) = [tex]\rho[/tex]a

^{3}/3epsilonR

^{3}[ 3

**R**[tex]\delta[/tex]/R

^{2}

**R**-[tex]\delta[/tex]]

I tried to use superposition and calculate E field due to each sphere and add up. But didn't get anywhere.

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