Let F= r k r, where r = x i+ y j+ z k and k is a constant . (Note that if k = − 3 , this is an inverse-square field.) Let σ be the sphere of radius a centered at the origin and oriented by the outward normal n = r / r = r / a . (a) Find the flux of F across σ without performing any integration . (b) For what value of k is the flux independent of the radius of the sphere?
Let F= r k r, where r = x i+ y j+ z k and k is a constant . (Note that if k = − 3 , this is an inverse-square field.) Let σ be the sphere of radius a centered at the origin and oriented by the outward normal n = r / r = r / a . (a) Find the flux of F across σ without performing any integration . (b) For what value of k is the flux independent of the radius of the sphere?
Let
F=
r
k
r,
where r
=
x
i+
y
j+
z
k
and
k
is a constant
.
(Note that if
k
=
−
3
,
this is an inverse-square field.) Let
σ
be the sphere of radius a centered at the origin and oriented by the outward normal
n
=
r
/
r
=
r
/
a
.
(a) Find the flux of F across
σ
without performing any integration.
(b) For what value of kis the flux independent of the radius of the sphere?
Quantities that have magnitude and direction but not position. Some examples of vectors are velocity, displacement, acceleration, and force. They are sometimes called Euclidean or spatial vectors.
Thomas' Calculus: Early Transcendentals (14th Edition)
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