Problem 8: An electric field E(x,y,z) = (xi + y-N(x²+y-)j+2zk) passes through the square that is parallel to the x-y plane with a side length of L that is centered on the z-axis at the position P,.

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Problem 8: An electric field E(x,y,z) = y(xi + y/N(x2+y²)j+ 2zk) passes
through the square that is parallel to the x-y plane with a side length of L that is
centered on the z-axis at the position P,.
Part (a) Integrate to find an expression for the total electric flux through the plane in terms of defined quantities and enter the expression.
Part (b) If the position P,= 43 m, side L = 4.1 m and the field strength per unit length is y = 434.4 V/m2, what is the numerical value for the flux in
volt meters?
Transcribed Image Text:Problem 8: An electric field E(x,y,z) = y(xi + y/N(x2+y²)j+ 2zk) passes through the square that is parallel to the x-y plane with a side length of L that is centered on the z-axis at the position P,. Part (a) Integrate to find an expression for the total electric flux through the plane in terms of defined quantities and enter the expression. Part (b) If the position P,= 43 m, side L = 4.1 m and the field strength per unit length is y = 434.4 V/m2, what is the numerical value for the flux in volt meters?
Expert Solution
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Here the area vector is pointing only along the z-direction and there are no components along x and y direction.

dS=dS k^=0i+0j+ dx dy kThe electric field E=γx i+γy2x2+y2j +γ2z kE.dS=(γx i+ γ y2jx2+y2+2γz k).( 0i+0j+dx dy k)         =2γ z dx dyϕ=E.dS=2γz0L dx 0L dy                    =2γz L2Answer: Part a, ϕ=2γz L2

 

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