Which, if either, of the two force fields F 1 = − y i + x j + z k , F 2 = y i + x j + z k is conservative? Calculate for each field the work done in moving a particle around the circle x = cos t , y = sin t in the ( x , y ) plane.
Which, if either, of the two force fields F 1 = − y i + x j + z k , F 2 = y i + x j + z k is conservative? Calculate for each field the work done in moving a particle around the circle x = cos t , y = sin t in the ( x , y ) plane.
Which, if either, of the two force fields
F
1
=
−
y
i
+
x
j
+
z
k
,
F
2
=
y
i
+
x
j
+
z
k
is conservative? Calculate for each field the work done in moving a particle around the circle
x
=
cos
t
,
y
=
sin
t
in the
(
x
,
y
)
plane.
Find the electric flux PE across the part of the cylinder x² + y² = 9,0 ≤ z ≤ 2, in the direction of the outer unit normal
vectors when the electric field is E = E(x, y, z) = xi + 2yj + 5zk.
(Express numbers in exact form. Use symbolic notation and fractions where needed.)
ΦΕ =
If the electric potential at a point (x, y) in the xy-plane is
V(x, y), then the electric intensity vector at the point (x, y)
is E = – vV(x, y). Suppose that V(x, y) = e¯2x cos 2y.
(a) Find the electric intensity vector at (x/4, 0).
(b) Show that at each point in the plane, the electric po-
tential decreases most rapidly in the direction of the
vector E.
Fundamentals of Differential Equations and Boundary Value Problems
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