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 If D = 2xy i + 3yz j + 4xz k, how much flux passes through x = 3 plane for which -1<y<2 and 0<z<4?
  • a)
    12
  • b)
    24
  • c)
    36
  • d)
    48
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
If D = 2xy i + 3yz j + 4xz k, how much flux passes through x = 3 plane...
Answer: c
Explanation: By Gauss law, ψ = ∫∫ D.ds, where ds = dydz i at the x-plane. Put x = 3 and integrate at -1<y<2 and 0<z<4, we get 12 X 3 = 36.
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Most Upvoted Answer
If D = 2xy i + 3yz j + 4xz k, how much flux passes through x = 3 plane...
To find the flux passing through the x = 3 plane, we need to find the dot product of the vector field D and the normal vector of the x = 3 plane.

The normal vector of the x = 3 plane is i.

Taking the dot product:

D · n = (2xy i + 3yz j + 4xz k) · i
= 2xy

Since x = 3, we can substitute this value into the equation:

D · n = 2(3)(y)
= 6y

So the flux passing through the x = 3 plane is 6y.
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