Step 1:

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Diameter of the two spheres is $\"\"$ .

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Radius of the sphere is $\"\"$ .

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Charge on first sphere is $\"\"$ .

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Charge on second sphere is $\"\"$ .

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Diastance between the two spheres is $\"\"$ .

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Total distance from center of the sphere to the mid point is $\"\"$ .

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$\"\"$ .

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Electric field due to charged particle is $\"image\"$ , where

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$\"image\"$ is the permittivity of free space $\"image\"$ .

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$\"\"$ is the charge of the electron.

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$\"\"$ is the distance between the two point charges.

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Find the electric field strength of the first sphere. $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"image\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The electric field strength of the first sphere is $\"\"$ .

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Step 2:

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Find the electric field strength of the second sphere. $\"\"$ .

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Substitute $\"\"$ , $\"\"$ and $\"image\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The electric field strength of the second sphere is $\"\"$ .

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Since mid point is considered , the magnitude of the right sphere contribution is also same as the left sphere and is in oppsit direction.

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$\"\"$

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$\"\"$ .

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$\"\"$ .

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Solution :

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Electric field

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Electric field strength at the midpoint between the two spheres is $\"\"$ .