Question

A large plane charge sheet having surface charge density σ=2.0×10−6 Cm−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∘ with the z-axis. (Given that the field due to infinite charged sheet is σ2ϵ0 where σ = surface charge density. Also note that it is perpendicular to the sheet and is constant for all points from the sheet.)

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Solution

The correct option is **C**

17.5 Nm2C

Now it is given that field is constant but area vector makes some angle with the direction of →E field. You clearly know that in such cases there is a simplified notation as.

ϕ=→E.→A

The normal to the x-y plane is the z axis and the electric field will be along the z axis. Now from the question, the angle between →E and →A is 600.

So, ϕ=→E→A cos 600

ϕ=σ2ϵ0×π(10−2)2×12=17.5 CNm2

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