Q 4. Confirm that ∇ (1/ r) = − r /r 3 where r = ||r e || and r e = xˆı + y ˆj + z kˆ = ρ eˆρ + z ...
Q 4. Confirm that ∇ (1/ r) = − r /r 3 where r = ||r e || and r e = xˆı + y ˆj + z kˆ = ρ eˆρ + z eˆz = r eˆr. Do it in (i) cartesian coordinates with ∇ ≡ ∂ ∂x ˆı + ∂ ∂y ˆ + ∂ ∂z kˆ. (ii) cylindrical coordinates with ∇ ≡ ∂ ∂ρ eˆρ + 1 ρ ∂ ∂φ eˆφ + ∂ ∂z eˆz. (iii) spherical coordinates with ∇ ≡ ∂ ∂r eˆr + 1 r ∂ ∂θ eˆθ + 1 r sin(θ) ∂ ∂φ eˆφ.
Homework Answers
Add Answer to:
Q 4. Confirm that ∇ (1/ r) = − r /r 3 where r = ||r e || and r e = xˆı + y ˆj + z kˆ = ρ eˆρ + z ...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z)...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z) and (p',p',z'), and Cartesian coordinates (x, y, z) and (x',y',z'), respectively. Write r - r in all three coordinate systems. Hint: Use Equation 1.2) with a r r and r and r' written in terms of appropriate unit vectors.
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) r...
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
Log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (...
log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (Write your answer in set notation.) (b) Find ▽f. (c) Find the tangent hyperplnes Te2)(r, y,z) and Tao2-)f(x, y, z). Find the intersection of these two hyperplanes, and very briefly describe the intersection in words (0,1, 1) and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2, 2, 1) is (d) On...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addi...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
PLE 2 The point (0, 5 3 , −5) is given in rectangular coordinates. Find spherical...
PLE 2 The point (0, 5 3 , −5) is given in rectangular coordinates. Find spherical coordinates for this point. SOLUTION From the distance formula we have ρ = x2 + y2 + z2 = 0 + 75 + 25 = 10 Correct: Your answer is correct. and so these equations give the following. cos(φ) = z ρ = -1/2 Correct: Your answer is correct. φ = $$ Incorrect: Your answer is incorrect. cos(θ) = x ρ sin(φ) = θ...
only do problem 3c, the second picture is the answer to problem 2, the answer I...
only do problem 3c, the second picture is the answer
to problem 2, the answer I got for 3b is -1/(r^2)
The tinction V(x, y,z) Problem 3 (20 pts). Considering the function V of problem 2, (a) Show that V can be written in spherical coordinates as V(r, θ, φ-1. (10 pts) r + θ + φ (b) The gradient of a function in spherical coordinates is VV Calculate the gradient of V in spherical coordinates. (5 pts) (e) Show...
1. Express the point given in Cartesian coordinates in cylindrical coordinates (r,θ,z). (9(√3/2), 9(1/2), 1)= 2....
1. Express the point given in Cartesian coordinates in
cylindrical coordinates (r,θ,z). (9(√3/2), 9(1/2), 1)=
2. Express the point given in Cartesian coordinates in spherical
coordinates (ρ,θ,ϕ). (7/3√3,21/4,7/2) =
I know we are only supposed to post 1 per question however for
this one I have 1 part correct, I just need some help with the
rest. Please if you have the time help with question 2. Thank you
for your time and knowledge.
(1 point) Express the point given...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment d located at the origin takes the following form d-T Tr where r is the vector joining the origin to the point X (7 is called the "position vector" in the textbook). See Fig. 2 (i) Chosing the z axis to be aligned with the electric dipole moment, express φ in terms of cartesian, cylindrical, (ii) The electric field is obtained from E-- Compute...
3. (i) Find the kinetic energy of a particle of mass m with position given by...
3. (i) Find the kinetic energy of a particle of mass m with position given by the coordinates (s, u, v), related to the ordinary Cartesian coordinates by y z = 2s + 3 + u = 2u + v = 0+03 (ii) Find the kinetic energy of a particle of mass m whose position is given in cylindrical coordinates = = r cos r sine y (iii) Find the kinetic energy of a particle of mass m with position...
Question 2. Comsider fcn log(2 - 2) (x2 + y2) (e) Find the level set of f which has value "height...
Question 2. Comsider fcn log(2 - 2) (x2 + y2) (e) Find the level set of f which has value "height") wo 0, and describe it in words and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2,2, 1) is perpendicular to this surface. (f) Using cylindrical and spherical coordinates find feyl(p,9,2) and fsm(r, θ, φ). (g) Express the cartesian point (V3,-v3,-v/2) in cylindrical and spherical coordinates. Use your answers to directly...
1.18. Points P and P' have spherical coordinates (r,0,y) and (r,θ,φ), cylindrical coordinates (p, p, z) and (p',p',z'), and Cartesian coordinates (x, y, z) and (x',y',z'), respectively. Write r - r in all three coordinate systems. Hint: Use Equation 1.2) with a r r and r and r' written in terms of appropriate unit vectors.
For the described solid S, write the triple integral f(x,y, z)dV as an iterated integral in (i) rectangular coordinates (x,y, z); (ii) cylindrical coordinates (r, 0, 2); (iii) spherical coordinates (p, φ,0). a. Inside the sphere 2 +3+224 and above the conezV b. Inside the sphere x2 + y2 + 22-12 and above the paraboloid z 2 2 + y2. c. Inside the sphere 2,2 + y2 + z2-2 and above the surface z-(z2 + y2)1/4 d. Inside the sphere...
log(2 - 2) (x2 y Question 2. Consider the function f(x, y, (a) What is the maximal domain of f? (Write your answer in set notation.) (b) Find ▽f. (c) Find the tangent hyperplnes Te2)(r, y,z) and Tao2-)f(x, y, z). Find the intersection of these two hyperplanes, and very briefly describe the intersection in words (0,1, 1) and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2, 2, 1) is (d) On...
A. Make a sketch of a vector F- (x,y, z), labeling the appropriate spherical coordinates. In addition, show the unit vectors r, θ, and φ at that point B. Write the vectors ŕ.0, and ф in terms of the unit vectors x, y, and г. Here's the easy way to do this 1. For r, simply use the fact that/r 2. For φ, use the following formula sin θ Explain why the above formula works 3. Compute θ via θ...
only do problem 3c, the second picture is the answer
to problem 2, the answer I got for 3b is -1/(r^2)
The tinction V(x, y,z) Problem 3 (20 pts). Considering the function V of problem 2, (a) Show that V can be written in spherical coordinates as V(r, θ, φ-1. (10 pts) r + θ + φ (b) The gradient of a function in spherical coordinates is VV Calculate the gradient of V in spherical coordinates. (5 pts) (e) Show...
1. Express the point given in Cartesian coordinates in
cylindrical coordinates (r,θ,z). (9(√3/2), 9(1/2), 1)=
2. Express the point given in Cartesian coordinates in spherical
coordinates (ρ,θ,ϕ). (7/3√3,21/4,7/2) =
I know we are only supposed to post 1 per question however for
this one I have 1 part correct, I just need some help with the
rest. Please if you have the time help with question 2. Thank you
for your time and knowledge.
(1 point) Express the point given...
FIG. 2. Setup of Exercise 3 Exercise 3 The electrostatic potential of an electic dipole moment d located at the origin takes the following form d-T Tr where r is the vector joining the origin to the point X (7 is called the "position vector" in the textbook). See Fig. 2 (i) Chosing the z axis to be aligned with the electric dipole moment, express φ in terms of cartesian, cylindrical, (ii) The electric field is obtained from E-- Compute...
3. (i) Find the kinetic energy of a particle of mass m with position given by the coordinates (s, u, v), related to the ordinary Cartesian coordinates by y z = 2s + 3 + u = 2u + v = 0+03 (ii) Find the kinetic energy of a particle of mass m whose position is given in cylindrical coordinates = = r cos r sine y (iii) Find the kinetic energy of a particle of mass m with position...
Question 2. Comsider fcn log(2 - 2) (x2 + y2) (e) Find the level set of f which has value "height") wo 0, and describe it in words and set notation. Confirm that the point (2, 2, 1) is on this level surface, and that Vf(2,2, 1) is perpendicular to this surface. (f) Using cylindrical and spherical coordinates find feyl(p,9,2) and fsm(r, θ, φ). (g) Express the cartesian point (V3,-v3,-v/2) in cylindrical and spherical coordinates. Use your answers to directly...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 11 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 11 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 11 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 11 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 11 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 11 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 11 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 11 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 11 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 11 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 11 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 11 months ago