Electrostatics problem involving infinite sheet

1. The problem statement, all variables and given/known data

An infinite dielectric sheet having charge density σ has a hole of radius R in it. An electron is released on the axis of the hole at a distance R√3 from the centre. What will be the velocity which it crosses the plane of sheet? (e = charge on electron and m = mass of electron)

2. Relevant equations

3. The attempt at a solution

Force at a distance x on the axis of the hole can be calculated by finding electric field at a distance x .Electric field is found by superimposing the electric field due to the sheet and the circular disk containing charge density -σ .

## E = \frac{σ}{2ε_0}\frac{x}{\sqrt{R^2+x^2}}##

##mv\frac{dv}{dx} = \frac{σ}{2ε_0}\frac{x}{\sqrt{R^2+x^2}}##

##vdv = \frac{σ}{2mε_0}\frac{x}{\sqrt{R^2+x^2}}dx##

Now integrating under proper limits I get incorrect answer .

Is this the correct way to approach the problem ?

I would be grateful if somebody could help me with the problem.

Attached Images
File Type: gif sheet.gif (3.3 KB)


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