a) ln(x2 + y2) calculate the Laplacian ∇2 of the scalar field using both cartesian and...

a) ln(x² + y²)

calculate the Laplacian ∇² of the scalar field using both cartesian and cylindrical coordinate systems

b) (x² + y² + z²)^-1/2

calculate the Laplacian ∇² of the scalar field using both cartesian and spherical coordinate systems

Expert Solution

Colby Messinger answered 10 months ago

2. Assume that the potential in Cartesian coordinates is given as V=x2-y2. According to this; (a)...

2. Assume that the potential in Cartesian coordinates is given as V=x2-y2. According to this; (a) The value of the potential at coordinate P (2, -1,3) (b) Electric field, the magnitude of the displacement vector and field lines (c) Calculate the charge density on the conductive surface

The set R^2 with addition and scalar multiplication defined by (x1, y1) + (x2, y2) =...

The set R^2 with addition and scalar multiplication defined by (x1, y1) + (x2, y2) = (x1 + x2, y1 + y2) c(x1, y1) = (cx1, y1) is not a vector space. Determine which axiom fails and find a counterexample that shows that it fails.

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2....

Consider the unit sphere x2 +y2 +z2 = 1 and the cone (z+√2)2 = x2 +y2. Show that these surfaces are tangent where they intersect, that is, for a point on the intersection, these surfaces have the same tangent plane

If C is the part of the circle (x2)2+(y2)2=1(x2)2+(y2)2=1 in the first quadrant, find the following...

If C is the part of the circle (x2)2+(y2)2=1(x2)2+(y2)2=1 in the first quadrant, find the following line integral with respect to arc length. ∫C(8x−6y)ds

Using the following data... (a) Fill in the table: X Y X2 Y2 XY 5 2...

Using the following data... (a) Fill in the table: X Y X2 Y2 XY 5 2 7 3 10 4 8 5 7 4 ΣX = ΣY = ΣX2 = ΣY2 = ΣXY = (b) Compute the degrees of freedom and determine the critical value of r for α = 0.05 (two-tails). df = r-critical = (c) Compute SSX, SSY, SP, and the Pearson correlation (r). (Use 3 decimals) SSX = SSY = SP = r = (d) What decision...

Si U=(x2+y2+z2)-1/2 , demuestre que ∂2U/∂x2+∂2U/∂y2+∂2U/∂z2=0

Let F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j...

Let F= (x2 + y + 2 + z2) i + (exp( x2 ) + y2) j + (3 + x) k . Let a > 0 and let S be part of the spherical surface x2 + y2 + z2 = 2az + 15a2 that is above the x-y plane and the disk formed in the x-y plane by the circular intersection between the sphere and the plane. Find the flux of F outward across S.

We define a relation ∼ on R^2 by (x1,y1)∼(x2,y2) if and only if (y2−y1) ∈ 2Z....

We define a relation ∼ on R^2 by (x1,y1)∼(x2,y2) if and only if (y2−y1) ∈ 2Z. Show that the relation∼is an equivalence relation and describe the equivalence class of the point (0,1).

Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of...

Let F(x,y,z) = < z tan-1(y2), z3 ln(x2 + 1), z >. Find the flux of F across S, the top part of the paraboloid x2 + y2 + z = 2 that lies above the plane z = 1 and is oriented upward. Note that S is not a closed surface.

1. The function f(x, y) = ln(x3 + 2) / (y2 + 3) (this function is...

1. The function f(x, y) = ln(x3 + 2) / (y2 + 3) (this function is of a fraction format) : a. has a stationary point at (1, 0) b. has a stationary point at (0, 0) c. has a stationary point at (0, 1) d. has no stationary points 2. Which of the following functions don’t have unit elasticity at P = 6? a. Demand: Qd = 24 - 2 P b. Demand: Qd = 10/P c. Demand: log...

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