Consider the following vector field. F = (xi + yj + zk )/((x^2 + y^2 + z^2)^3/2) (a) Find the divergence of F. (b) Let S...
Consider the following vector field. F = (xi + yj + zk )/((x^2 + y^2 + z^2)^3/2)
(a) Find the divergence of F.
(b) Let S be any sphere not containing the origin. Find the outward flux of F across S.
(c) Let Sa be the sphere of radius a centered at the origin. Find the outward flux of F across Sa.
Homework Answers
Add Answer to:
Consider the following vector field. F = (xi + yj + zk )/((x^2 + y^2 + z^2)^3/2) (a) Find the divergence of F. (b) Let S...
xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or...
xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or more conveniently, (.x2 + y2 + 22)3/2 1 Fr) where r = xi + yj + zk and r= ||1|| = x2 + y2 + x2 (instead of p) 73 r (a) [10 pts) Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral [/F F.Nds where S is the unit sphere 22 + y2 + z2 1...
13. Use the divergence theorem to evaluate Sis Fonds where F(x, y, z) - Xi+yj+zk and...
13. Use the divergence theorem to evaluate Sis Fonds where F(x, y, z) - Xi+yj+zk and S is the unit cube in the first octant bounded by the planes x-0, x= 1, y = 0, y - 1,2-0, z - 1. The vector n is the unit outward normal to the cube.
zi+yj + zk 3. Given the vector field in space F(x, y, z) or more conveniently,...
zi+yj + zk 3. Given the vector field in space F(x, y, z) or more conveniently, (x2 + y2 + 22)3/2 f where r = ci + yj + zk and r= |||| = V2 + y2 + z2 (instead of p) 1 F(r) = r2 (a) [10 pts] Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral lle F.NDS where S is the unit sphere x2 + y2 + z2 = 1...
Let F = xi + yj + zk, and let D be the cube bounded by...
Let F = xi + yj + zk, and let D be the cube bounded by the
planes x = y = z = +-1. Let S be the boundary of D. Verify the
divergence theorem...
1, and z 1. 3. Let F-zi +yj + zk, and let D be the cube bounded by the planes x-+1, y planes cl, Let S be the boundary of D. Verify the Divergence Theorem by showing JJJD
Let F(x, y, z) = xi + yj + zk and S be the surface defined...
Let F(x, y, z) = xi + yj + zk and S be the surface defined by z = 9 – 22 - y2 and 2 > 0. Evaluate SsFinds, where n is the upward unit normal vector.
can you solve this vector problems? Find the outward flux of the vector field F(x, y,...
can you solve this vector problems?
Find the outward flux of the vector field F(x, y, z) = (xi + yj
+ zk)/(x 2 + y 2 + z 2 ) 3/2 across the ellipsoid 4x^2 + 9y^2 + z^2
= 1.
6. (12 pts.) Find the outward flux of the vector field F(r,y, ) (ri yj+ zk)/(x2 + y2 22)3/2 across the ellipsoid 4r2 +9y2 + z2 = 1
6. (12 pts.) Find the outward flux of the vector...
9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj +...
9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj + zk. (a) 67T (d) 0 (b) 1 (e) None of these (c) 3π
9. Let Q be the solid bounded by the cylinder x2 + y2...
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its...
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its divergence G. (2) Let H R3 -> R3 be given as H(x,y, z) = (1,2,3). Find a vector potential A : R3 -> R3 such that curl(A) smooth function = H. Show that if A is a vector potential for H, then so is A+ Vf, for any f : R5 -> R (3) Let...
across Let F = (x i+yj +z k'). What is the outward flux of F (x2...
across Let F = (x i+yj +z k'). What is the outward flux of F (x2 + y2 +22)8 a sphere of radius R> 0 centered at the origin?
#4 please 3. (12 pts). (a) (8 pts) Directly compute the flux Ф of the vector field F-(x + y)1+ yj + zk over the closed surface S given by z 36-x2-y2 and z - 0. Keep in mind that N is the outward...
#4 please
3. (12 pts). (a) (8 pts) Directly compute the flux Ф of the vector field F-(x + y)1+ yj + zk over the closed surface S given by z 36-x2-y2 and z - 0. Keep in mind that N is the outward normal to the surface. Do not use the Divergence Theorem. Hint: Don't forget the bottom! (b) (4 pts) Sketch the surface. ts). Use the Divergence Theorem to compute the flux Ф of Problem 3. Hint: The...
xi+ yj + zk 3. Given the vector field in space F(x, y, z) = or more conveniently, (.x2 + y2 + 22)3/2 1 Fr) where r = xi + yj + zk and r= ||1|| = x2 + y2 + x2 (instead of p) 73 r (a) [10 pts) Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral [/F F.Nds where S is the unit sphere 22 + y2 + z2 1...
13. Use the divergence theorem to evaluate Sis Fonds where F(x, y, z) - Xi+yj+zk and S is the unit cube in the first octant bounded by the planes x-0, x= 1, y = 0, y - 1,2-0, z - 1. The vector n is the unit outward normal to the cube.
zi+yj + zk 3. Given the vector field in space F(x, y, z) or more conveniently, (x2 + y2 + 22)3/2 f where r = ci + yj + zk and r= |||| = V2 + y2 + z2 (instead of p) 1 F(r) = r2 (a) [10 pts] Find the divergence of F, that is, V.F. (b) (10 pts] Directly evaluate the surface integral lle F.NDS where S is the unit sphere x2 + y2 + z2 = 1...
Let F = xi + yj + zk, and let D be the cube bounded by the
planes x = y = z = +-1. Let S be the boundary of D. Verify the
divergence theorem...
1, and z 1. 3. Let F-zi +yj + zk, and let D be the cube bounded by the planes x-+1, y planes cl, Let S be the boundary of D. Verify the Divergence Theorem by showing JJJD
Let F(x, y, z) = xi + yj + zk and S be the surface defined by z = 9 – 22 - y2 and 2 > 0. Evaluate SsFinds, where n is the upward unit normal vector.
can you solve this vector problems?
Find the outward flux of the vector field F(x, y, z) = (xi + yj
+ zk)/(x 2 + y 2 + z 2 ) 3/2 across the ellipsoid 4x^2 + 9y^2 + z^2
= 1.
6. (12 pts.) Find the outward flux of the vector field F(r,y, ) (ri yj+ zk)/(x2 + y2 22)3/2 across the ellipsoid 4r2 +9y2 + z2 = 1
6. (12 pts.) Find the outward flux of the vector...
9. Let Q be the solid bounded by the cylinder x2 + y2 = 1 and the planes z = 0 and z = 1 . Use the Divergence Theorem to calculate | | F . N dS where s is the surface of Q and F(x, y, z) = xi + yj + zk. (a) 67T (d) 0 (b) 1 (e) None of these (c) 3π
9. Let Q be the solid bounded by the cylinder x2 + y2...
(1) Let G(,y, z) = (x,y, z). Show that there exists no vector field A : R3 -> R3 such that curl(A) Hint: compute its divergence G. (2) Let H R3 -> R3 be given as H(x,y, z) = (1,2,3). Find a vector potential A : R3 -> R3 such that curl(A) smooth function = H. Show that if A is a vector potential for H, then so is A+ Vf, for any f : R5 -> R (3) Let...
across Let F = (x i+yj +z k'). What is the outward flux of F (x2 + y2 +22)8 a sphere of radius R> 0 centered at the origin?
#4 please
3. (12 pts). (a) (8 pts) Directly compute the flux Ф of the vector field F-(x + y)1+ yj + zk over the closed surface S given by z 36-x2-y2 and z - 0. Keep in mind that N is the outward normal to the surface. Do not use the Divergence Theorem. Hint: Don't forget the bottom! (b) (4 pts) Sketch the surface. ts). Use the Divergence Theorem to compute the flux Ф of Problem 3. Hint: The...
Most questions answered within 3 hours.
-
Write a program to solve the Josephus problem, with the following
modification:
Sample Input:
./a.out n...
asked 1 minute ago -
At the start of a CD it is spinning at a rate of 525 rpm
(revolutions...
asked 37 minutes ago -
4. Without doing any calculations, predict whether the observed
∆T would increase, decrease or remain the...
asked 1 hour ago -
Based on the range, which of the following sets of scores has
the greatest variability? 3,...
asked 3 hours ago -
Ripples in a pond travel at a velocity of 3 m/s with one peak
passing a...
asked 2 hours ago -
A man stands on the roof of a building of height 13.0 mm and
throws a...
asked 2 hours ago -
The extent to which assets are financed by borrowed funds and
other liabilities is indicated by:...
asked 3 hours ago -
Explain in detail
Germany is the fifth largest economy
explain what goods and services Germany specializes...
asked 4 hours ago -
The density of platinum is 21.45 g/mL. If a cube of platinum
with a mass of...
asked 4 hours ago -
Accounts Receivable
Sales
A/R Posting
Extended Sales Invoice
Packing Slip
Compare invoice to packing slip 2...
asked 4 hours ago -
Michaella, age 23, is a full-time law student and is claimed by
her parents as a...
asked 4 hours ago -
Why are polymers not typically casted into products?
asked 4 hours ago