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A large nonconducting sheet M is given a...

A large nonconducting sheet M is given a uniform charge density. Two unchared small metal rods A and B are placed near the sheet as shown in figure

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We can consider two sheets of thickness `(t/2-x)` and `(t/2+x)`
When a point lies inside the sheet.
Net electric field at point `P : E=E_(1)-E_(2)=Q_(1)/(2Aepsi_(0))-Q_(2)/(2Aepsi_(0))`
[`Q_(1)` : charge on left sheet, `Q_(2=` change of right sheet]
`=(AP (t/2+x)-2rhoA(t/2-x))/(2Aepsi_(0))=(rho[3x-t/2])/(2epsi_(0))`
At the symmetry plane, `x=0` So, `E=-(rho t)/(4 epsi_(0))`
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