How do you evaluate an integral using stokes theorem if the curve given is a unit circle in a plane z=α [closed]

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So, C is given as a unit circle in the plane z=α, how would I evaluate this when the formula for stokes asks for the normal vector of a curve but given a slice of a cylinder?

multivariable-calculus

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asked Jul 30 at 6:17

edmonda7

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closed as off-topic by Xander Henderson, Adrian Keister, José Carlos Santos, Jyrki Lahtonen, Lord Shark the Unknown Jul 31 at 14:09

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  Please take the time to formulate your problem completely. We are no clairvoyants.
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So, C is given as a unit circle in the plane z=α, how would I evaluate this when the formula for stokes asks for the normal vector of a curve but given a slice of a cylinder?

multivariable-calculus

share|cite|improve this question

asked Jul 30 at 6:17

edmonda7

163

closed as off-topic by Xander Henderson, Adrian Keister, José Carlos Santos, Jyrki Lahtonen, Lord Shark the Unknown Jul 31 at 14:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Adrian Keister, José Carlos Santos

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please take the time to formulate your problem completely. We are no clairvoyants.
  – Christian Blatter
  Jul 30 at 7:42
  

  
  
  
  

add a comment | 

up vote
1
down vote

favorite

up vote
1
down vote

favorite

So, C is given as a unit circle in the plane z=α, how would I evaluate this when the formula for stokes asks for the normal vector of a curve but given a slice of a cylinder?

multivariable-calculus

share|cite|improve this question

asked Jul 30 at 6:17

edmonda7

163

So, C is given as a unit circle in the plane z=α, how would I evaluate this when the formula for stokes asks for the normal vector of a curve but given a slice of a cylinder?

multivariable-calculus

share|cite|improve this question

asked Jul 30 at 6:17

edmonda7

163

share|cite|improve this question

share|cite|improve this question

asked Jul 30 at 6:17

edmonda7

163

asked Jul 30 at 6:17

edmonda7

163

asked Jul 30 at 6:17

edmonda7

163

163

closed as off-topic by Xander Henderson, Adrian Keister, José Carlos Santos, Jyrki Lahtonen, Lord Shark the Unknown Jul 31 at 14:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Adrian Keister, José Carlos Santos

If this question can be reworded to fit the rules in the help center, please edit the question.

closed as off-topic by Xander Henderson, Adrian Keister, José Carlos Santos, Jyrki Lahtonen, Lord Shark the Unknown Jul 31 at 14:09

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – Xander Henderson, Adrian Keister, José Carlos Santos

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please take the time to formulate your problem completely. We are no clairvoyants.
  – Christian Blatter
  Jul 30 at 7:42
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  

  
  
  
  
  
  

  
  Please take the time to formulate your problem completely. We are no clairvoyants.
  – Christian Blatter
  Jul 30 at 7:42
  

  
  
  
  

Please take the time to formulate your problem completely. We are no clairvoyants.
– Christian Blatter
Jul 30 at 7:42

Please take the time to formulate your problem completely. We are no clairvoyants.
– Christian Blatter
Jul 30 at 7:42

add a comment | 

1 Answer
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The Stokes Theorem states that
$$oint_C vecF cdot dvecr = iint_S nabla times vecF cdot dvecS = iint_S nabla times vecF cdot vecn; dS, $$
where $S$ is any surface bounded by $C$, with normal unit vector $vecn$.

In your case, $C$ is a unit circle in the plane $z=alpha$, so a good choice is to consider the surface $S$ as the disc inside $C$, that is :
beginalign
&x = r cos theta \
&y = r sin theta quad quad mboxwithquad 0le r le 1, ; 0le theta le 2 pi\
&z= alpha
endalign

The normal unit vector $vecn$ is trivially $(0,0,1)$, which should simplify calculations.

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answered Jul 30 at 9:01

Kuifje

6,8112523

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1 Answer
1

active

oldest

votes

1 Answer
1

active

oldest

votes

active

oldest

votes

active

oldest

votes

up vote
1
down vote

The Stokes Theorem states that
$$oint_C vecF cdot dvecr = iint_S nabla times vecF cdot dvecS = iint_S nabla times vecF cdot vecn; dS, $$
where $S$ is any surface bounded by $C$, with normal unit vector $vecn$.

In your case, $C$ is a unit circle in the plane $z=alpha$, so a good choice is to consider the surface $S$ as the disc inside $C$, that is :
beginalign
&x = r cos theta \
&y = r sin theta quad quad mboxwithquad 0le r le 1, ; 0le theta le 2 pi\
&z= alpha
endalign

The normal unit vector $vecn$ is trivially $(0,0,1)$, which should simplify calculations.

share|cite|improve this answer

answered Jul 30 at 9:01

Kuifje

6,8112523

add a comment | 

up vote
1
down vote

The Stokes Theorem states that
$$oint_C vecF cdot dvecr = iint_S nabla times vecF cdot dvecS = iint_S nabla times vecF cdot vecn; dS, $$
where $S$ is any surface bounded by $C$, with normal unit vector $vecn$.

In your case, $C$ is a unit circle in the plane $z=alpha$, so a good choice is to consider the surface $S$ as the disc inside $C$, that is :
beginalign
&x = r cos theta \
&y = r sin theta quad quad mboxwithquad 0le r le 1, ; 0le theta le 2 pi\
&z= alpha
endalign

The normal unit vector $vecn$ is trivially $(0,0,1)$, which should simplify calculations.

share|cite|improve this answer

answered Jul 30 at 9:01

Kuifje

6,8112523

add a comment | 

up vote
1
down vote

up vote
1
down vote

The Stokes Theorem states that
$$oint_C vecF cdot dvecr = iint_S nabla times vecF cdot dvecS = iint_S nabla times vecF cdot vecn; dS, $$
where $S$ is any surface bounded by $C$, with normal unit vector $vecn$.

In your case, $C$ is a unit circle in the plane $z=alpha$, so a good choice is to consider the surface $S$ as the disc inside $C$, that is :
beginalign
&x = r cos theta \
&y = r sin theta quad quad mboxwithquad 0le r le 1, ; 0le theta le 2 pi\
&z= alpha
endalign

The normal unit vector $vecn$ is trivially $(0,0,1)$, which should simplify calculations.

share|cite|improve this answer

answered Jul 30 at 9:01

Kuifje

6,8112523

The Stokes Theorem states that
$$oint_C vecF cdot dvecr = iint_S nabla times vecF cdot dvecS = iint_S nabla times vecF cdot vecn; dS, $$
where $S$ is any surface bounded by $C$, with normal unit vector $vecn$.

In your case, $C$ is a unit circle in the plane $z=alpha$, so a good choice is to consider the surface $S$ as the disc inside $C$, that is :
beginalign
&x = r cos theta \
&y = r sin theta quad quad mboxwithquad 0le r le 1, ; 0le theta le 2 pi\
&z= alpha
endalign

The normal unit vector $vecn$ is trivially $(0,0,1)$, which should simplify calculations.

share|cite|improve this answer

answered Jul 30 at 9:01

Kuifje

6,8112523

share|cite|improve this answer

share|cite|improve this answer

answered Jul 30 at 9:01

Kuifje

6,8112523

answered Jul 30 at 9:01

Kuifje

6,8112523

answered Jul 30 at 9:01

Kuifje

6,8112523

6,8112523

add a comment | 

add a comment |