Physics For Scientists And Engineers 6E - part 190
19.
An infinitely long line charge having a uniform charge per
unit length 3 lies a distance d from point O as shown in
Figure P24.19. Determine the total electric flux through
the surface of a sphere of radius R centered at O resulting
from this line charge. Consider both cases, where R , d
and R - d.
20. An uncharged nonconducting hollow sphere of radius
10.0 cm surrounds a 10.0-%C charge located at the origin
of a cartesian coordinate system. A drill with a radius of
1.00 mm is aligned along the z axis, and a hole is drilled in
the sphere. Calculate the electric flux through the hole.
21. A charge of 170 %C is at the center of a cube of edge
80.0 cm. (a) Find the total flux through each face of the
cube. (b) Find the flux through the whole surface of the
cube. (c) What If? Would your answers to parts (a) or
(b) change if the charge were not at the center? Explain.
22.
The line ag in Figure P24.22 is a diagonal of a cube. A
point charge q is located on the extension of line ag, very
close to vertex a of the cube. Determine the electric flux
through each of the sides of the cube which meet at the
point a.
Section 24.3 Application of Gauss’s Law to Various
Charge Distributions
23. Determine the magnitude of the electric field at the
surface of a lead-208 nucleus, which contains 82 protons
and 126 neutrons. Assume the lead nucleus has a volume
208 times that of one proton, and consider a proton to be
a sphere of radius 1.20 & 10
'
15
m.
24.
A solid sphere of radius 40.0 cm has a total positive charge
of 26.0 %C uniformly distributed throughout its volume.
Calculate the magnitude of the electric field (a) 0 cm,
(b) 10.0 cm, (c) 40.0 cm, and (d) 60.0 cm from the center
of the sphere.
25. A 10.0-g piece of Styrofoam carries a net charge of
'
0.700 %C and floats above the center of a large horizon-
tal sheet of plastic that has a uniform charge density on its
surface. What is the charge per unit area on the plastic
sheet?
26.
A cylindrical shell of radius 7.00 cm and length 240 cm has
its charge uniformly distributed on its curved surface. The
magnitude of the electric field at a point 19.0 cm radially
outward from its axis (measured from the midpoint of the
shell) is 36.0 kN/C. Find (a) the net charge on the shell
and (b) the electric field at a point 4.00 cm from the axis,
measured radially outward from the midpoint of the shell.
27.
A particle with a charge of ' 60.0 nC is placed at the
center of a nonconducting spherical shell of inner radius
20.0 cm and outer radius 25.0 cm. The spherical shell
carries charge with a uniform density of ' 1.33 %C/m
3
.
A proton moves in a circular orbit just outside the
spherical shell. Calculate the speed of the proton.
28. A nonconducting wall carries a uniform charge density of
8.60 %C/cm
2
. What is the electric field 7.00 cm in front of
the wall? Does your result change as the distance from the
wall is varied?
Consider a long cylindrical charge distribution of
radius R with a uniform charge density 1. Find the electric
field at distance r from the axis where r , R.
30. A solid plastic sphere of radius 10.0 cm has charge with uni-
form density throughout its volume. The electric field
5.00 cm from the center is 86.0 kN/C radially inward. Find
the magnitude of the electric field 15.0 cm from the center.
Consider a thin spherical shell of radius 14.0 cm with a
total charge of 32.0 %C distributed uniformly on its
surface. Find the electric field (a) 10.0 cm and (b) 20.0 cm
from the center of the charge distribution.
32. In nuclear fission, a nucleus of uranium-238, which
contains 92 protons, can divide into two smaller spheres,
each having 46 protons and a radius of 5.90 & 10
'
15
m.
What is the magnitude of the repulsive electric force
pushing the two spheres apart?
33. Fill two rubber balloons with air. Suspend both of them
from the same point and let them hang down on strings of
equal length. Rub each with wool or on your hair, so that
they hang apart with a noticeable separation from each
other. Make order-of-magnitude estimates of (a) the force
on each, (b) the charge on each, (c) the field each creates
at the center of the other, and (d) the total flux of electric
field created by each balloon. In your solution state the
quantities you take as data and the values you measure or
estimate for them.
34.
An insulating solid sphere of radius a has a uniform
volume charge density and carries a total positive charge
Q. A spherical gaussian surface of radius r, which shares a
common center with the insulating sphere, is inflated
starting from r # 0. (a) Find an expression for the electric
flux passing through the surface of the gaussian sphere as
a function of r for r , a. (b) Find an expression for the
electric flux for r - a. (c) Plot the flux versus r.
A uniformly charged, straight filament 7.00 m in length has
a total positive charge of 2.00 %C. An uncharged cardboard
cylinder 2.00 cm in length and 10.0 cm in radius surrounds
the filament at its center, with the filament as the axis of
the cylinder. Using reasonable approximations, find (a) the
electric field at the surface of the cylinder and (b) the total
electric flux through the cylinder.
36. An insulating sphere is 8.00 cm in diameter and carries
a 5.70-%C charge uniformly distributed throughout its
interior volume. Calculate the charge enclosed by a
concentric spherical surface with radius (a) r # 2.00 cm
and (b) r # 6.00 cm.
A large flat horizontal sheet of charge has a charge per
unit area of 9.00 %C/m
2
. Find the electric field just above
the middle of the sheet.
37.
35.
31.
29.
Problems
757
d
c
a
b
e
f
g
h
q
Figure P24.22