Calculating Electric Field at Point P on a Uniformly Charged Surface

AI Thread Summary
The discussion focuses on calculating the electric field at point P, located a distance z from the center of a circular hole cut from a uniformly charged nonconducting surface with surface charge density sigma. The approach involves using the principle of superposition, where the electric field from the entire charged surface is reduced by the field from the charged disc representing the hole. The proposed formula for the electric field at point P is E = (σ/2ε₀) - (σ/2ε₀)(1 - z/√(z² + R²)), simplifying to E = (σz)/(2ε₀√(z² + R²)). The calculations appear to be correct, and the method aligns with the hint provided. This approach effectively addresses the problem of finding the electric field at point P.
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A large flat nonconducting surface carries a uniform surface charge density of sigma. A small circular hole of radius R has been cut out from this surface as in the figure. Ignore the fringing of the fierld lines around all the edges and calculate the electric field at point P located a distance z from the centre of the hole. (Hint says to refer to the electric field due to a charged disc and use superposition)

well I am using the hint and thinking that the field would the electric field due to a nonconducting surface less the electric field due to this charged disc.

so would it be E = \frac{\sigma}{2\epsilon_{0}} - \frac{\sigma}{2\epsilon_{0}} (1- \frac{z}{\sqrt{z^2+r^2}}) = \frac{\sigma z}{2 \epsilon_{0} \sqrt{z^2+R^2}}
is this correct? PLease do advise! Thank you!
 

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Looks good to me.
 
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