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A rectangular pipe, running parallel to the z-axis (from −∞ to ∞) has three grounded metal sides, at y=0 and x=0. The fourth side, at x=b, is maintained at a specified potential V0(y). Develop a general formula for the potential inside the pipe. Find the potential explicitly, for the case V0(y)=V 0 ​ (a constant).

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Ankit Lal
Ankit LalLv10
25 Feb 2021
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Related textbook solutions

Physics: Principles with Applications
7th Edition, 2013
Giancoli
ISBN: 9780321625922

Related questions

Consider a long conducting pipe shown in cross section.


Fig 5.1 A square conducting pipe shown in cross section. The axisofthe pipe is the z axis, pointing out of the page


Let the walls at x=+/- a/2 be grounded (V=0) and the walls aty =+/- a/2 be held at equal but opposite potentials +/- V0.

(a) Determine V(x,y). (Hint...exploit te idea that it is anoddfunction of y.)
(b) Plot the potential V(0,y) versus y. Let V0 be the unitofpotential and a the unit of length. (computerprogram to be used because the result of (a) is aninfinite serieswhich must be evaluated numerically.
(c) Calculate the electric field at the origin.

An infinite metal slab is located perpendicular to thex-axis, between x = 0 and x = 2.0 cm(see figure). The slab has a surface charge density of +7.6 × 10-6C/m2 on each side.

(a) Find the magnitude of the potentialdifference between x = 0 and x = 3.5 cm.

|V(3.5 cm) - V(0)| =V

For parts (b) and (c), take the potential to be 0 at x= 0.

(b) What is the potential at x = 2.0 cm?.

V(2.0 cm) = V

(c) What is the potential at x = 3.5 cm?.

V(3.5 cm) = V

For parts (d) and (e), take the potential to be 0 at x= -3.5 cm.

(d) What is the potential at x = 2.0 cm?.

V(2.0 cm) = V

(e) What is the potential at x = 5.5 cm?.

V(5.5 cm) = V

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