Question

3. A semi-infinite pipe runs parallel to the positive $x$ axis. It has grounded sides at $y = 0$, $y = a$, $z = 0$, and $z = b$, while the end at $x = 0$ is held at the potential $V_0(y, z) = \sin(2\pi y/a)$. Use separation of variables to find the potential inside the pipe.

Name: 3. A semi-infinite pipe runs parallel to the positive x axis. It has grounded sides at y = 0, y = a, z = 0, and z = b, while the end at x = 0 is held at the potential V0(y, z) = sin(2π y/a). Use separation of variables to find the potential inside the pipe.
Uploaded: 2022-11-13T04:34:15-08:00
Duration: 1 min 59 s
Channel: Sri K
Description: 3. A semi-infinite pipe runs parallel to the positive x axis. It has grounded sides at y = 0, y = a, z = 0, and z = b, while the end at x = 0 is held at the potential V0(y, z) = sin(2π y/a). Use separation of variables to find the potential inside the pipe.

          3. A semi-infinite pipe runs parallel to the positive $x$ axis. It has grounded sides at $y = 0$, $y = a$, $z = 0$, and $z = b$, while the end at $x = 0$ is held at the potential $V_0(y, z) = \sin(2\pi y/a)$. Use separation of variables to find the potential inside the pipe.

3. A semi-infinite pipe runs parallel to the positive x axis. It has grounded sides at y = 0, y = a, z = 0, and z = b, while the end at x = 0 is held at the potential V0(y, z) = sin(2π y/a). Use separation of variables to find the potential inside the pipe.

Added by Meagan C.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

11/13/2022

Step 1

Let's call these functions X(x), Y(y), and Z(z). Therefore, the potential inside the pipe can be written as V(x, y, z) = X(x)Y(y)Z(z). Show more…

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3.A semi-infinite pipe runs parallel to the positive axis.It has grounded sides at y=0.y az=0,andz=b,while the end atx=0 is held at the potential Voy,z=sin2ry/a Use separation of variables to find the potential inside the pipe.