A cube has sides of length L = 0.400 m . It is placed with one corner at the ori

Question

A cube has sides of length L = 0.400 m . It is placed with one corner at the origin as shown in the figure (Figure 1) . The electric field is not uniform but is given by E =( -5.71 N/(Cm) )xi^+( 3.20 N/(Cm) )zk^.

Please show the solutions with steps.

Problem 22.34 A cube has sides of length L 30.400 m. It is placed with one comer at the origin as shown in the figure (Figure The electric field is not uniform but is given by E (-5.71 )zi+ (3.20 N/(C m) )zk Figure 1 of 1 S2 (top) (back) So S (right side) (left side) S (bottom Ss (front) Part A Find the electric flux through each of the six cube faces S,So, Sa, S4,Ss, and S6. Enter your answers in ascending order separated by commas. Submit My Answers Give Incorrect, Try Again; 4 attempts remaining Part B Find the total electric charge inside the cube. Submit My Answers Gve UO N/C)-mi Provide Feedback Continue

Explanation / Answer

Let's call -5.71 N/(C m) = a and 3.20 N/(C m) = b,

so
E = a x i + b z k

S1: only the x component,

but x=0 everywhere on that surface:

flux = Surface-integral = 0

S2: only the z-component "pierces"through there, and since z=L on that surface:

Surface_integral = b L * L^2 = b L^3

S3: same as S2 but with only x-component and x = L there => a L^3

S4 (bottom) : only z-component of field pierces,

but z=0 there,

so : 0
S5 and S6 would need a y component of the field, but since that's zero: 0

adding these contributions gives: (a + b ) L^3, and according to Maxwell's first theorem in integral form:
Q = eps0 (a+b) L^3.

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