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A large plane charge sheet having surfac...

A large plane charge sheet having surface xharge density `sigma=2.0 xx 10^(-6) C m^(-2)` lies in the x-y plane. Find the flux of the electric field through a circular area of radius 1 cm lying completely in the region where x, y, z are all positive and with its normal making an angle of `60^0` with the z-axis.

Text Solution

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the electric field near the poane charge sheet is `E=sigma/2epsilon_0` in the direction away from the sheet. At the given area, the field is along the z-axis.
The area `=pir^2=3.14 xx 1 cm^2=3.14 xx 10^(-4) m^2`.
The angle between the normal to the area and the field is `60^0`.
Hence, the flux `=VecE DeltaS = EDeltaS cosTheta=sigma/2epsilon_0`
`2.0 xx 10^(-6) C m^(-2)/2 xx 8.85 xx 10^(-12) C^2 N m^(-1) xx (3.14 xx 10^(-4) m^2)1/2
`=17.5N m^2 C^(-1)`.
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