Question

2. The following vector field \textbf{E}, passes through an open spherical surface, defined below. Evaluate the integral, shown below: \textbf{E} = 2r \sin\theta \cos\phi \mathbf{a}_r X = \iint \textbf{E} \cdot d\textbf{s} where: d\textbf{s} = differential surface of the sphere defined by r = 3, 30^\circ < \theta \le 45^\circ, 45^\circ < \phi \le 90^\circ

          2. The following vector field \textbf{E}, passes through an open spherical surface, defined below.
Evaluate the integral, shown below:
\textbf{E} = 2r \sin\theta \cos\phi \mathbf{a}_r

X = \iint \textbf{E} \cdot d\textbf{s}

where:

d\textbf{s} = differential surface of the sphere defined by r = 3, 30^\circ < \theta \le 45^\circ, 45^\circ < \phi \le 90^\circ

2. The following vector field E, passes through an open spherical surface, defined below.
Evaluate the integral, shown below:
E = 2r sinθcosϕ𝐚r

X = ∬E ·ds

where:

ds = differential surface of the sphere defined by r = 3, 30^∘< θ≤45^∘, 45^∘< ϕ≤90^∘

Added by Carolina P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zack A

07/08/2023

Step 1

The differential surface area element for a sphere in spherical coordinates is given by ds = r^2sin(θ)dθdφ, where r is the radius of the sphere. Show more…

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The following vector field E, passes through an open spherical surface, defined below. Evaluate the integral, shown below: E=2rsin heta cosphi a_(r) x=∬E*ds where: ds= differential surface of the sphere defined by r=3,30deg < heta <=45deg ,45deg <phi <=90deg 2. The following vector field E, passes through an open spherical surface, defined below Evaluate the integral, shown below: E =2r sin 0 cos a X= E.ds where: ds = differential surfaceof the sphere defined by r =3, 30 <0 45, 45< 90