A cube has sides of length L = 0.320 m. It is placed with one corner at the origin. The electric field is not uniform but is given by E= ( -5.02 N/(C*m))xi +(3.04 N/(C*m))zk.
A) Find the electric flux through each of the six cube faces S1 (left side), S2 (top), S3 (right side), S4 (bottom), S5 (front), and S6 (back).
B) Find the total electric charge inside the cube.
Any help is greatly appreciated!
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Let’s call -5.02 N/(C m) = a and 3.04 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.
You can plug in the numbers (remember that a is a negative number..)
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