Question

In: Physics

A long conducting pipe has a rectangular cross section with sides of lengths a and b....

A long conducting pipe has a rectangular cross section with sides of lengths a and b. One face of the pipe is maintained at a constant potential V = V0 while the other 3 faces are grounded (V = 0). Using separation of variables, find the potential for points inside the pipe V (x,y).

Solutions

Expert Solution

please upvote ? if you like my answer ?


Related Solutions

2) Imagine an infinitely long hollow metal pipe with a rectangular cross section. The four sides...
2) Imagine an infinitely long hollow metal pipe with a rectangular cross section. The four sides are placed at x = −a and x = a, and at y = −b and y = b. The two sides on the x-axis (and parallel to the y-z plane) are held at V = 0, the two sides on the y-axis (and parallel to the x-z plane) are held at a constant positive potential V = V0. Imagine that each infinite plate...
An infinitely long, solid non-conducting rod (cylinder) with circular cross section of radius a has its...
An infinitely long, solid non-conducting rod (cylinder) with circular cross section of radius a has its axis along the z-axis. It has a non-uniform volume charge density given in cylindrical coordinates by ρ(s) = C (s/a)^2 ,where C is a positive constant. In addition, there is a uniform volume charge density −σ on the outer cylindrical shell of radius b, where σ is a positive constant. Region 2 is a vacuum. For parts (a) through (c), use Gauss’ Law and...
BackgroundConsider a trianglewith sides of lengths a, b, and c where c is the...
BackgroundConsider a triangle with sides of lengths a, b, and c where c is the longest side. We can describe the side and angle properties of the triangle using these lengths.The side properties include:scalene if all three sides have a different lengthisosceles if two of the sides have the same lengthequilateral if all three sides have the same lengthThe Pythagorean Theorem determines the angle properties which include:acute if all angles are acute (<90 2="" or="">c**2right if one angle is right...
In a rectangular cross-section canal with a width of 10 m and a depth of 1.5...
In a rectangular cross-section canal with a width of 10 m and a depth of 1.5 m, uniform and Continuous current monitoring is applied. The channel's Manning coefficient includes 0.015. Base because its slope is 0.0005. Considering this information a) By writing the numerical magnitude of water face slope and energy line slope and its rationale Set. b) Calculate the speed of the current in the channel. c) Calculate the flow of the current in the channel. d ) When...
A water trough is 8 m long and has a cross-section in the shape of an...
A water trough is 8 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 80 cm wide at the top, and has height 50 cm. If the trough is being filled with water at the rate of 0.1 m3/min how fast is the water level rising when the water is 40 cm deep?
A water trough is 8 m long and has a cross-section in the shape of an...
A water trough is 8 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 70 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.3 m3/min how fast is the water level rising when the water is 20 cm deep?
A 2024-T3 aluminum bar has rectangular cross section dimensions of 2" x 0.5". The length of...
A 2024-T3 aluminum bar has rectangular cross section dimensions of 2" x 0.5". The length of the column is 9.0 inches. A) Calculate the transition slenderness ratio (Sr)D for this column. [Answer should be 69.9] B) Calculate the slenderness ratio for your assigned column length. [Answer should be 62] C) Calculate the maximum unit load (Pcr/A) for the bar. Indicate whether the column is a Johnson or Euler column. [Numerical answer should be 25296 psi but I don't know Johnson...
A long rectangular conducting loop of width 30 cm is partially in a region of a...
A long rectangular conducting loop of width 30 cm is partially in a region of a horizontal magnetic field of 1.74 T perpendicular to the loop, as shown in the figure below. The mass of the loop is 14 g, and its resistance is 0.17 . If the loop is released, what is its terminal velocity? Assume that the top of the loop stays in the magnetic field. (Hint: The terminal velocity occurs when the magnetic force on the induced...
A rectangular cross section beam (A) made of steel constructed in an industrial building between two...
A rectangular cross section beam (A) made of steel constructed in an industrial building between two columns which are “X” m apart. The beam is acting as a support for one end of a pair of crane wheel (B). The distance b/w wheels are “Y” m. The crane is used to lift max. of Z tonnes of load which is having hook at the centre of crane. Draw shear force and B.M diagram of the beam. Case i) If the...
A rectangular cross section beam (A) made of steel constructed in an industrial building between two...
A rectangular cross section beam (A) made of steel constructed in an industrial building between two columns which are “X” m apart. The beam is acting as a support for one end of a pair of crane wheel (B). The distance b/w wheels are “Y” m. The crane is used to lift max. of Z tonnes of load which is having hook at the centre of crane. Draw shear force and B.M of all types of beam diagram of the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT