Question

Find the total charge enclosed in a cube defined by: 0<x<1, 0<y<2, and 0<z<2. With charge density: rho= 2xyz (micro coulomb/m^3).

Answer #1

Consider a cube 1< x,y,z < 2
and D=4x2yx+xy3y
C/m2
a) what is the volume charge density
b) what is the total charge enclosed in the cube
c) what is the flux of ΦD leaving the surface of the
cube

the region enclosed by the cylinder x^2+y^2=64 and the planes
z=0 and x+y+z=16

A cube of side 2a, centered at the origin and with the x, y, and
z axes perpendicular to the faces of the cube, carries a frozen-in
polarization of P = czzˆ, where c is a constant. Note that the
magnitude of P is not constant – it is a function of z.
(a) Find the total bound charge inside the cube, and the total
bound charge on each surface of the cube. The sum of all charges
should add...

find the volume of the solid enclosed by the two paraboloids
y=x^2+z^2 and y=2-x^2-z^2

The average value of a function f(x, y, z) over a solid region E
is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the
volume of E. For instance, if ρ is a density function, then ρave is
the average density of E. Find the average value of the function
f(x, y, z) = 5x2z + 5y2z over the region enclosed by the paraboloid
z = 4 − x2 − y2 and the...

1. Find the area of the region enclosed between y=4sin(x) and
y=4cos(x) from x=0 to x=0.5π
2. Find the volume of the solid formed by rotating the region
enclosed by
x=0, x=1, y=0, y=8+x^5
about the x-axis.
3. Find the volume of the solid obtained by rotating the region
bounded by
y=x^2, y=1.
about the line y=7.

consider the joint density function
Fx,y,za (x,y,z)=(x+y)e^(-z) where 0<x<1, 0<y<1,
z>0
find the marginal density of z : fz (z).
hint. figure out which common distribution Z follows and report
the rate parameter
integral (x+y)e^(-z) dz
(x+y)(-e^(-z) + C
is my answer 1. ???

An unknown positive point charge is placed at x = -0.36 m, y = 0
m, a charge of -4.8 micro-coulombs is placed at x = 0 m, y = -0.23
m, a charge of +2.4 micro-coulombs is placed at x = +0.37 m, y =
-0.2 m, and charge of +4.8 micro-coulombs is placed at x = 0 m, y =
+0.23 m. If the total electric field due to all four charges at the
origin is 3.9 x...

Let f(x,y)=1 for 0<x<1, 0<y<1 and 0 otherwise. Find
the probability density function of Z=max(X, Y)

Let f(x,y)=1 for 0<x<1, 0<y<1 and 0 otherwise. Find
the probability density function of Z=max(X, Y)

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