Consider a thin flat rectangular region that of size 4 x 2 m2 and it is...

Consider a thin flat rectangular region that of size 4 x 2 m2 and it is electrically insulated at its four corners. (A)Solve Laplace’s equation  2 V(x,y) = 0 in the rectangular region 0 < x < 4 m and 0 < y < 2 m using the separation of variable technique subject to the following boundary conditions:
V(0,y) = 0
V(4,y) = q(y) = 50 sin (3π y / 2)
V(x,0) = 0
V(x,2) = f(x) =100 sin (π x / 4)
(B) Use the result of part (A) to find the corresponding electric field inside the region.

Solutions

Expert Solution

Manojponduru answered 1 month ago

Next > < Previous

Related Solutions

A thin rectangular plate coincides with the region defined by 0 ≤ x ≤ π, 0...

A thin rectangular plate coincides with the region defined by 0 ≤ x ≤ π, 0 ≤ y ≤ 1. The left end and right end of the plate are insulated. The bottom of the plate is held at temperature zero and the top of the plate is held at temperature f(x) = 4 cos(6x) + cos(7x). Set up an initial-boundary value problem for the steady-state temperature u(x, y).

The flat circular plate has the shape of the region ? 2 + ? 2 ≤...

The flat circular plate has the shape of the region ? 2 + ? 2 ≤ 4. The plate, including the boundary ? 2 + ? 2 = 4, is heated so that the temperature at the point (x, y) is: ?(?, ?) = ? 2 + ? 2 − 2? + 1. Find the temperatures at the hottest and coldest points on the plate.

Consider a very long rectangular fin attached to a flat surface such that the temperature at...

Consider a very long rectangular fin attached to a flat surface such that the temperature at the end of the fin is essentially that of the surrounding air, i.e. 20°С. Its width is 5.0 cm; thickness is 1.0 mm; thermal conductivity is 200 W/m·K; and base temperature is 40°C. The heat transfer coefficient is 20 W/m2 .K. You can use Table 1(a) for assistance. (i) Estimate the fin temperature at a distance of 5.0 cm from the base, and; (ii)...

What is the probability of finding the particle in the region a/4 < x < a/2?...

What is the probability of finding the particle in the region a/4 < x < a/2? show your work.

Consider the region bounded by cos(x2) and the x−axis for 0 ≤ x ≤ ?(π/2)^1/2 ....

Consider the region bounded by cos(x2) and the x−axis for 0 ≤ x ≤ ?(π/2)^1/2 . If this region is revolved about the y-axis, find the volume of the solid of revolution. (Note that ONLY the shell method works here).

Find the area of the region enclosed by the graphs of y^2 = x + 4...

Find the area of the region enclosed by the graphs of y^2 = x + 4 and y^2 = 6 − x

Find the area of the region bounded by the parabolas x = y^2 - 4 and...

Find the area of the region bounded by the parabolas x = y^2 - 4 and x = 2 - y^2 the answer is 8 sqrt(3)

1. Consider the region bounded by the graph of y^2 = r^2 −x^2 (a) When this...

1. Consider the region bounded by the graph of y^2 = r^2 −x^2 (a) When this region is rotated about the x-axis a sphere of radius r is generated. Use integration to find its volume V (b) Use integration to find the surface area of such a sphere 2. Find the arc length of the curve y = 1 3 x 3/2 on [0, 60] ( 3. Consider the graph of y = x^3 . Compute the surface area of...

Consider the region bounded between y = 3 + 2x - x^2 and y = e^x...

Consider the region bounded between y = 3 + 2x - x^2 and y = e^x + 2 . Include a sketch of the region (labeling key points) and use it to set up an integral that will give you the volume of the solid of revolution that is obtained by revolving the shaded region around the x-axis, using the... (a) Washer Method (b) Shell Method (c) Choose the integral that would be simplest to integrate by hand and integrate...

Consider the region R enclosed between the curves y = 2 /x and y = 1,...

Consider the region R enclosed between the curves y = 2 /x and y = 1, between x = 1 and x = 2. Calculate the volume of the solid obtained by revolving R about the x-axis, (a) using cylindrical shells; (b) using washers

Subjects