Question

The cube in thefigure has sides of length L = 10.0 cm . The electric field is uniform, has a magnitude E = 4.00 * 10^3 N/C, and is parallel to the xy-plane at an angle of 36.9degrees measured from the + x axis toward the + y axis.

a.What is the electric flux through the cube face S_1?

b. What is the electric flux through the cube face S_2?

c. What is the electric flux through the cube face S_3?

d. What is the electric flux through the cube face S_4?

e. What is the electric flux through the cube face S_5?

f. What is the electric flux through the cube face S_6?

g. What is the total electric flux through all faces of the cube?

Answer 1

We have electric fluxΦ = E A cosθ

given E = 4*10³N/CArea A = (10*10^-2m)(10*10^-2m) =0.01m²θ is the angle made by the electric field with the normalto the surface.A) For the surface S₁normal to the surface is -yaxis.here the electric field makes an angle 36.9^owiththe positive x - axis. therefore angle made by the electric fieldwith the y-axis is90^o-36.9^o=53.1^otherefore the angle made by the electric field with the normalto the surface S₁is 180^o+ 53.1^o= 233.1^oThenΦ₁=(4*10³N/C)(0.01m²)(cos233.1^o)=-24Nm²/CB) For the surface S₁normal to the surface isz axis.as the elcetric field is parallel to the XY plane thereforetheangle made by the electric field with the z-axis is90^otherefore the angle made by the electric field with the normalto the surface S₂is 90^oThenΦ₂=(4*10³N/C)(0.01m²)(cos90^o)=0Nm²/CC) For the surface S₃normal to the surface isy axis.here the electric field makes an angle 36.9^owiththe positive x - axis. therefore angle made by the electric fieldwith they-axis is90^o-36.9^o=53.1^otherefore the angle made by the electric field with the normalto the surface S₃is 53.1^oThenΦ₃=(4*10³N/C)(0.01m²)(cos53.1^o)=24Nm²/CD)For the surface S₄normal to thesurface is z axis.as the elcetric field is parallel to the XY plane thereforetheangle made by the electric field with the z-axis is90^otherefore the angle made by the electric field with the normalto the surface S₄is 90^oThenΦ₄=(4*10³N/C)(0.01m²)(cos90^o)=0Nm²/CE) For the surface S₅normal to the surface isx axis.here the electric field makes an angle 36.9^owiththe positive x - axis.therefore the angle made by theelectricfield with the normal to the surface S₅is36.9^{oThenΦ₅=(4*103N/C)(0.01m2)(cos36.9o)}=32Nm²/CF) For the surface S₆normal to the surface is-x axis.here the electric field makes an angle 36.9^owiththe positive x - axis.therefore the angle made bytheelectric field with the normal to the surface S₆is180^o+36.9^o=216.9^oThenΦ₆=(4*10³N/C)(0.01m²)(cos216.9^o)=-32Nm²/CG)Total electric flux isΦ=Φ₁+Φ₂+Φ₃+Φ₄+Φ₅+Φ_{6= 0Nm²/C}