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GATE Electronics and Communications (EC) 2013 Solved Paper
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Question : 12 of 65
Marks:
+1
,
-0
Consider a vector field
A
⃗
(
r
⃗
)
\vec{A}(\vec{r})
A
(
r
)
. The closed loop line integral
∮
A
⃗
⋅
d
l
⃗
\oint \vec{A} \cdot \vec{dl}
∮
A
⋅
d
l
can be expressed as
∯
s
(
∇
×
A
⃗
)
⋅
d
s
⃗
\oiint_{s} (\nabla \times \vec{A}) \cdot \vec{ds}
∬
s
(
∇
×
A
)
⋅
d
s
over the closed surface bounded by the loop.
∭
(
∇
⋅
A
⃗
)
d
v
\iiint (\nabla \cdot \vec{A}) \, dv
∭
(
∇
⋅
A
)
d
v
over the closed volume bounded by the loop.
∭
(
∇
⋅
A
⃗
)
d
v
\iiint (\nabla \cdot \vec{A}) \, dv
∭
(
∇
⋅
A
)
d
v
over the open volume bounded by the loop.
∬
(
∇
×
A
⃗
)
⋅
d
s
⃗
\iint (\nabla \times \vec{A}) \cdot \vec{ds}
∬
(
∇
×
A
)
⋅
d
s
. over the open surface bounded by the loop.
Validate
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