Poll Results
No votes. Be the first one to vote.
Lost your password? Please enter your email address. You will receive a link and will create a new password via email.
Please briefly explain why you feel this question should be reported.
Please briefly explain why you feel this answer should be reported.
Please briefly explain why you feel this user should be reported.
No votes. Be the first one to vote.
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.
To solve this, we’ll use the concept of flux through a surface. The flux (Phi) of a vector field (textbf{D} = Ptextbf{i} + Qtextbf{j} + Rtextbf{k}) through a surface (S) is given by the surface integral of (textbf{D} cdot textbf{n} dS), where (textbf{n}) is the unit normal to the surface and (dS) is a differential element of the surface area.
Given (textbf{D} = 2xy textbf{i} + 3yz textbf{j} + 4xz textbf{k}) and considering the plane (x = 3) with (-1 < y < 2) and (0 < z < 4), we'll calculate the flux through this plane area.
For the plane (x = 3), the normal vector is parallel to the (textbf{i}) direction since the plane is perpendicular to the x-axis. Therefore, only the component of (textbf{D}) in the direction of (textbf{i}) contributes to the flux through this plane.
The relevant component of (textbf{D}) here is (P = 2xy), and since (x = 3), we have (P = 6y). The