If F(r) = c r 3 r is an inverse-square field, and if σ is a closed orientable surface that surrounds the origin, then Gauss’s law states that the outward flux of F across σ is _________ . On the other hand, if σ does not surround the origin, then that it follows from the Divergence Theorem that the outward flux of F across σ is _________ .
If F(r) = c r 3 r is an inverse-square field, and if σ is a closed orientable surface that surrounds the origin, then Gauss’s law states that the outward flux of F across σ is _________ . On the other hand, if σ does not surround the origin, then that it follows from the Divergence Theorem that the outward flux of F across σ is _________ .
If
F(r)
=
c
r
3
r
is an inverse-square field, and if
σ
is a closed orientable surface that surrounds the origin, then Gauss’s law states that the outward flux of F across
σ
is
_________
.
On the other hand, if
σ
does not surround the origin, then that it follows from the Divergence Theorem that the outward flux of F across
σ
is
_________
.
(c) Ifo and are smooth scalar fields, show that
▼x (6V) = Vox V
X
For each of the following vector fields, find its curl and determine if it is a gradient field.
(a) ♬ = 5yz i + (5xz + z²) j + (5xy+2yz) k
curl F
F?
=
(b) Ğ = (10xy + x³) i+ (5x² + z²) j + (2yz – 4z) k
curl G
G ?
=
(c) H = 5yzi+ (z² – 5xz) j + (5xy + 2yz) k:
curl H
H?
=
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RELATIONS-DOMAIN, RANGE AND CO-DOMAIN (RELATIONS AND FUNCTIONS CBSE/ ISC MATHS); Author: Neha Agrawal Mathematically Inclined;https://www.youtube.com/watch?v=u4IQh46VoU4;License: Standard YouTube License, CC-BY