Evaluate $int vec{F}.ndS$ where $S$ is the entire surface of the solid formed by?
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Evaluate $int vec{F}.ndS$ where $S$ is the entire surface of the solid formed by $x^2+y^2=a^2, z=x+1, z=0$ and $n$ is the outward drawn unit normal and the vector function $vec{F}=langle2x,-3y,zrangle$
My question is, can I directly apply the divergence theorem in this?
Using the divergence theorem, since divergence of F is zero, we are getting zero.
vector-analysis vector-fields
asked Jan 10 at 12:51
learning_mathslearning_maths
587
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add a comment |
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Evaluate $int vec{F}.ndS$ where $S$ is the entire surface of the solid formed by $x^2+y^2=a^2, z=x+1, z=0$ and $n$ is the outward drawn unit normal and the vector function $vec{F}=langle2x,-3y,zrangle$
My question is, can I directly apply the divergence theorem in this?
Using the divergence theorem, since divergence of F is zero, we are getting zero.
vector-analysis vector-fields
asked Jan 10 at 12:51
learning_mathslearning_maths
587
$endgroup$
$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
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– DonAntonio
Jan 10 at 13:11
add a comment |
$begingroup$
Evaluate $int vec{F}.ndS$ where $S$ is the entire surface of the solid formed by $x^2+y^2=a^2, z=x+1, z=0$ and $n$ is the outward drawn unit normal and the vector function $vec{F}=langle2x,-3y,zrangle$
My question is, can I directly apply the divergence theorem in this?
Using the divergence theorem, since divergence of F is zero, we are getting zero.
vector-analysis vector-fields
asked Jan 10 at 12:51
learning_mathslearning_maths
587
$endgroup$
Evaluate $int vec{F}.ndS$ where $S$ is the entire surface of the solid formed by $x^2+y^2=a^2, z=x+1, z=0$ and $n$ is the outward drawn unit normal and the vector function $vec{F}=langle2x,-3y,zrangle$
My question is, can I directly apply the divergence theorem in this?
Using the divergence theorem, since divergence of F is zero, we are getting zero.
vector-analysis vector-fields
vector-analysis vector-fields
asked Jan 10 at 12:51
learning_mathslearning_maths
587
asked Jan 10 at 12:51
learning_mathslearning_maths
587
asked Jan 10 at 12:51
learning_mathslearning_maths
587
asked Jan 10 at 12:51
learning_mathslearning_maths
587
asked Jan 10 at 12:51
learning_mathslearning_maths
587
587
$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
$endgroup$
– DonAntonio
Jan 10 at 13:11
add a comment |
$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
$endgroup$
– DonAntonio
Jan 10 at 13:11
$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
$endgroup$
– DonAntonio
Jan 10 at 13:11
$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
$endgroup$
– DonAntonio
Jan 10 at 13:11
add a comment |
1 Answer
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You can apply the divergence theorem here. $$nablacdotvec F=Big(frac{partial}{partial x},frac{partial}{partial y},frac{partial}{partial z}Big)cdotbig(2x,-3y,zbig)=2-3+1=0$$giving the answer $0$.
answered Jan 10 at 16:52
Shubham JohriShubham Johri
4,885717
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1 Answer
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1 Answer
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$begingroup$
You can apply the divergence theorem here. $$nablacdotvec F=Big(frac{partial}{partial x},frac{partial}{partial y},frac{partial}{partial z}Big)cdotbig(2x,-3y,zbig)=2-3+1=0$$giving the answer $0$.
answered Jan 10 at 16:52
Shubham JohriShubham Johri
4,885717
$endgroup$
add a comment |
$begingroup$
You can apply the divergence theorem here. $$nablacdotvec F=Big(frac{partial}{partial x},frac{partial}{partial y},frac{partial}{partial z}Big)cdotbig(2x,-3y,zbig)=2-3+1=0$$giving the answer $0$.
answered Jan 10 at 16:52
Shubham JohriShubham Johri
4,885717
$endgroup$
add a comment |
$begingroup$
You can apply the divergence theorem here. $$nablacdotvec F=Big(frac{partial}{partial x},frac{partial}{partial y},frac{partial}{partial z}Big)cdotbig(2x,-3y,zbig)=2-3+1=0$$giving the answer $0$.
answered Jan 10 at 16:52
Shubham JohriShubham Johri
4,885717
$endgroup$
You can apply the divergence theorem here. $$nablacdotvec F=Big(frac{partial}{partial x},frac{partial}{partial y},frac{partial}{partial z}Big)cdotbig(2x,-3y,zbig)=2-3+1=0$$giving the answer $0$.
answered Jan 10 at 16:52
Shubham JohriShubham Johri
4,885717
edited Jan 10 at 16:57
answered Jan 10 at 16:52
Shubham JohriShubham Johri
4,885717
answered Jan 10 at 16:52
Shubham JohriShubham Johri
4,885717
answered Jan 10 at 16:52
Shubham JohriShubham Johri
4,885717
4,885717
add a comment |
add a comment |
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$begingroup$
I can't see why wouldn't you be able to use the divergence theorem...
$endgroup$
– DonAntonio
Jan 10 at 13:11