The cube in the figure Figure 1 has sides of length 145cm T

The cube in the figure (Figure 1) has sides of length 14.5cm .

The electric field is uniform, has a magnitude 1442NC , and is parallel to the xy-plane at an angle of 10.2 N/C, measured from the +x axis toward the +y axis.

Where A is a vector of magnitude the area of the side and direction perpendicular out from the side.  What is the electric flux through the cube face S1(left)? What is the electric flux through the cube face S2? (top) What is the electric flux through the cube face S3?(right side) What is the electric flux through the cube face S4? (bottom) What is the electric flux through the cube face S5? (front) What is the electric flux through the cube face S6? (back) What is the total electric flux through all faces of the cube?

Solution

phi = E A cos theta

E = 1442 N/C

A = L² = (14.5 * 10^-2m)(14.5 * 10^-2m) = 0.021 m²

a) For the surface S₁ normal to the surface is -yaxis.

The electric field makes an angle 10.2^o with the positive x - axis

Therefore angle made by the electric field with the y-axis = 90^o-10.2^o = 79.8^o

The angle made by the electric field with the normal to the surface S₁ = 180^o + 79.8^o= 259.8^o

phi₁ = (1442N/C)(0.021m²)(cos 259.8^o)

= - 5.36 Nm²/C

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b) For the surface S₂ normal to the surface is z axis.

As the elcetric field is parallel to the XY plane

Therefore the angle made by the electric field with the z-axis = 90^o

phi₂ = (1442 N/C)(0.021m²)(cos90^o)

= 0 Nm²/C

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c) For the surface S₃ normal to the surface isy axis.

Angle made by the electric fieldwith the y-axis = 90^o-10.2^o = 79.8^o

Therefore the angle made by the electric field with the normal to the surface S₃ = 79.8^o

phi₃ = (1442N/C)(0.021m²)(cos 79.8^o)

phi₃ = 5.36 Nm²/C

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d) For the surface S₄ normal to thesurface is z axis.

As the elcetric field is parallel to the XY plane , the angle made by the electric field with the z-axis = 90^o

phi₄ = (1442 N/C)(0.021m²)(cos 90^o)

phi₄ = 0 Nm²/C

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e) For the surface S₅ normal to the surface isx axis.

Here the electric field makes an angle 36.9^o with the positive x - axis

Therefore the angle made by theelectric field with the normal to the surface S₅ = 10.2

phi₅ =(1442 N/C)(0.021 m²)(cos 10.2)

= 29.8 Nm²/C

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f) For the surface S₆ normal to the surface is-x axis.

here the electric field makes an angle 10.2^o with the positive x - axis.

Therefore the angle made by theelectric field with the normal to the surface S₆ =180^o + 10.2^o =190.2^o

phi₆ = (1442 N/C)(0.021 m²)(cos 190.2^o)

= -29.8 Nm²/C

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g)Total electric flux is = phi₁+ phi₂ + phi₃+ phi₄ + phi₅+ phi₆

= 0 Nm²/C