Q19P Use equations (9.2), (9.8), and ... [FREE SOLUTION]

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Chapter 10: Q19P (page 528)

Use equations (9.2), (9.8), and (9.11) to evaluate the following expressions. In spherical coordinates $鈭� 脳 (r e_{胃}), 鈭� (r c o s 胃), 鈭� . r$ .

Short Answer

Expert verified

The required values are mentioned below.

$鈭� 脳 (r {\hat{e}}_{胃}) = 2 r {\hat{e}}_{蠒} 鈭� (r \cos 胃) = \cos 胃 {\hat{e}}_{r} - \sin 胃 {\hat{e}}_{蠒} 鈭� 路 r = 3$

Step by step solution

Definition of spherical coordinates.

The coordinate system primarily utilized in three-dimensional systems is the spherical coordinates of the system. The spherical coordinate system is used to find the surface area in three-dimensional space.

Determining the value of ∇×(reθ),∇(rcosθ),∇.r

Findthe value of $鈭� 脳 (r {\hat{e}}_{胃})$ .

role="math" localid="1659261996986" $鈭� 脳 (r {\hat{e}}_{胃}) = - \frac{1}{r^{2} \sin 胃鈭� 蠒} (r^{2}) {\hat{e}}_{r} + \frac{1}{r} \frac{鈭�}{鈭� r} r^{2} {\hat{e}}_{蠒} 鈭� 脳 (r {\hat{e}}_{胃}) = 2 r {\hat{e}}_{蠒}$

Findthe value of .

role="math" localid="1659262028625" $鈭� (r \cos 胃) = \frac{鈭�}{鈭� r} (r \cos 胃) {\hat{e}}_{r} + \frac{1}{r} \frac{鈭�}{鈭� 胃} (r \cos 胃) {\hat{e}}_{r} 鈭� (r \cos 胃) = \cos 胃 {\hat{e}}_{r} - \sin 胃 {\hat{e}}_{r}$

Findthe value of .

$鈭� 鈰� r = \frac{1}{r^{2} s i n 胃} \frac{鈭�}{鈭� r} (r^{2} s i n 胃 r) = 3$

The required values are mentioned below.

role="math" localid="1659262073399" $鈭� 脳 (r {\hat{e}}_{胃}) = 2 r {\hat{e}}_{蠒} 鈭� (r \cos 胃) = \cos 胃 {\hat{e}}_{r} - \sin 胃 {\hat{e}}_{r} 鈭� 鈰� r = \frac{1}{r^{2} s i n 胃} \frac{鈭�}{鈭� r} (r^{2} s i n 胃 r) = 3$

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91影视

Use equations (9.2), (9.8), and (9.11) to evaluate the following expressions. In spherical coordinates $鈭� 脳 (r e_{胃}), 鈭� (r c o s 胃), 鈭� . r$ .

Short Answer

Step by step solution

Definition of spherical coordinates.

Determining the value of ∇×(reθ),∇(rcosθ),∇.r

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Most popular questions from this chapter

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91影视

Use equations (9.2), (9.8), and (9.11) to evaluate the following expressions. In spherical coordinates 鈭�脳(re胃),鈭�(rcos胃),鈭�.r.

Short Answer

Step by step solution

Definition of spherical coordinates.

Determining the value of ∇×(reθ),∇(rcosθ),∇.r

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Solid State Physics

Scientific Method Physics

Energy Physics

Torque and Rotational Motion

Waves Physics

Magnetism and Electromagnetic Induction

Study anywhere. Anytime. Across all devices.

Use equations (9.2), (9.8), and (9.11) to evaluate the following expressions. In spherical coordinates $鈭� 脳 (r e_{胃}), 鈭� (r c o s 胃), 鈭� . r$ .