Part A Given a cube with sides parallel to the coordinate axes, with one corner

Question

Part A

Given a cube with sides parallel to the coordinate axes, with one corner at the origin (as in the figure (Figure 1) ), and with sides of length 1.8 m , estimate the flux out of the cube using a spreadsheet or other numerical method.

Express your answer using two significant figures.

Part B

How much total charge is enclosed by the cube?

Express your answer using two significant figures.

_total = Nm^2/C   An electric field is given by zty z ty Ezoe where E 69 N/C E. 38 N/C, and a 1.8 m Figure 1 of 1 dz

Explanation / Answer

Let the electric flux enter the cube via E1 and move out the cube through the face E2

Then total electric flux in the cube = E= E2 - E1

again from Gauss law electric flux = integration of E.ds = Q/ where S is the surface area and is the permittivity For cube the flux is Ea^2

where E= Ex0 exp-(x+y/a)^2 i'+ Ey0 exp-(x+y/a)^2 j'

putting values E= 69 exp-(x+y/1.8)^2 i' + 38 exp-(x+y/1.8)^2 j'

Total flux= 69 exp-(x+y/1.8)^2 i' + 38 exp-(x+y/1.8)^2 j' * 1.8^2 = 3.24[69 exp-(x+y/1.8)^2 i' + 38 exp-(x+y/1.8)^2 j' ]

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