Homework declare

The figure shows a closeup of the door Gaussian surface ar in the form of a cube the edge size 3.20 m. That lies in a an ar where the electric field is offered by E=(1.65x+2.86)i + 4.39j + 5.47k N/C, with x in meters. What is the network charge included by the cube?

Homework Equations

net flux= qenc/Eo (Gauss"s Law)Net flux= Ecos(theta)AA= r^2

The effort at a Solution

The top, bottom and sides don"t matter because they"re constant, therefore I must only need to look in ~ the front and also back. For the front next I had actually net flux = 2.86(cos (0deg))(10.24)=29.2864For the ago side I had net flux = (1.65*3.2+2.86)(cos 180deg)(10.24) = -83.3536So the total net flux would certainly be -54.0672.Multiply this number through 8.55e-12 and also I acquired the net fee to it is in -4.62275e-10. Any help would it is in appreciated.

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What is the worth of ##x## top top the back face (including sign)?##epsilon_0## is ##8.85 imes 10^-12 fracC^2N m^2##, not ##8.55 imes 10^-12 fracC^2N m^2##.
okay for this reason x is heading backwards right into the negative direction. For this reason the earlier face should be (1.65*-3.2+2.86)(cos 180deg)(10.24) = 83.3536the total net flux is then 83.3536+29.2864 = 112.64112.64*8.85e-12= 9.96864e-10C for my net charge?That doesn"t seem like it works either
Did you get 24.781? I can have simply took the original 83 number and also flipped the sign. Alright 24.7808+29.2864=54.067254.0672*8.85e-12 is 4.78495e-10C
Well, my approach to the equipment was just take the aberration of the electric field and also integrate over the volume.
Well, my approach to the systems was just take the aberration of the electrical field and integrate end the volume.
What execute you acquire when you shot to carry out it that way? I"m really no very an excellent at calc so the wouldn"t it is in my go to.

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Did you obtain 24.781? I can have simply took the initial 83 number and flipped the sign.alright 24.7808+29.2864=54.067254.0672*8.85e-12 is 4.78495e-10C
coils technique is nice, if girlfriend are acquainted with the aberration equation because that the electrical field. Girlfriend might consider how many far-ranging figures you must keep in her answer.
$$vec abla . vecE = ho/varepsilon_0$$Now because that the calculation of the LHS, us have;$$eginsplitvec abla .vecE &= left(fracpartialpartial xhatx + fracpartialpartial yhaty + fracpartialpartial zhatz ight) . left(left(1.65x + 2.86 ight)hatx + 4.39haty + 5.47hatz ight)\&= fracpartial left(1.65x + 2.86 ight)partial x + fracpartial left(4.39 ight)partial y + fracpartial left(5.47 ight)partial z\&= 1.65endsplit$$Multiply with the ##varepsilon_0## and also integrate end the volume of the cube as,$$eginsplitQ &= int dxdydz left(1.65varepsilon_0 ight)\&= 1.65varepsilon_0left(2.30 ight)^3\&= 4.7849 imes 10^-10 Cendsplit$$