HW5 Solutions
Notice numbers may change randomly in your assignments and
you may have to recalculate solutions for your specific case.
Tipler 21.P.018
Estimate the force required to bind the two protons in the He
nucleus together. (Hint: Model the protons as point charges.
Assume the diameter of the He nucleus to be approximately
10-15 m.)
Solution:
Since the nucleus is in equilibrium:
2
Fbinding = Felectrostatics " Fbinding
!
9
$19
kq 2 9 #10 # (1.6 #10 )
= 2 =
= 0.23kN
2
r
(10$15 )
Tipler 21.P.023
What is the total charge of all the protons in 1.50 kg of carbon?
Solution:
Carbon has Z = 6 protons hence Q = 6nCe, where nc = the
number of atoms in m = 0.20 kg of carbon. Since NA = Avogadro
number = number of Carbon atoms in a mole = number of
atoms in M = 12 g of Carbon-12 = 6.022 x 1023 atoms/mol:
NA : M = nC : m " nC =
mN A
mN A
" Q = 6e
= 7.23 #10 7 C
M
M
Tipler 21.P.028
!
A 2.0 µC point charge and a 4.0 µC point charge are a distance L
apart. Where should a third point charge be placed so that the
electric force on that third charge is zero?
Solution:
q2
q4
q3
x
L-x
Tipler 21.P.035
Five identical point charges, each having charge Q, are equally
spaced on a semicircle of radius R as shown in the figure below.
Find the force (in terms of k, Q, and R) on a charge q located
equidistant from the five other charges. (Use the following
variables as necessary: Q, R, q, k, i for , and j for .)
Solution:
Tipler 21.P.069
A rigid 1.00 m long rod is pivoted about its center. A charge q1 =
5.00 10-7 C is placed on one end of the rod, and a charge q2 = q1 is placed a distance d = 10.0 cm directly below it.
(a) What is the force exerted by q2 on q1?
(b) What is the torque (measured about the rotation axis) due to
that force?
(c) To counterbalance the attraction between the two charges,
we hang a block 25.0 cm from the pivot as shown. What value
should we choose for the mass m of the block?
(d) We now move the block and hang it a distance of 25.0 cm
from the balance point, on the same side of the balance as the
charge. Keeping q1 the same, and d the same, what value should
we choose for q2 to keep this apparatus in balance?
Solution:
Tipler 21.P.060
A dipole of moment 0.50 e · nm is placed in a uniform electric
field with a magnitude of 4.0 104 N/C. What is the magnitude of
the torque on the dipole for each of the following situations?
(a) the dipole is aligned with the electric field
(b) the dipole is transverse to (perpendicular to) the electric field
(c) the dipole makes an angle of 30.0° with the direction of the
electric field
(d) Defining the potential energy to be zero when the dipole is
transverse to the electric field, find the potential energy of the
dipole in the electric field for the orientations specified in Parts
(a) and (c).
Solution:
Tipler 21.P.051
The acceleration of a particle in an electric field depends on q/m
(the charge-to-mass ratio of the particle).
(a) Compute q/m for an electron.
(b) What are the magnitude and direction of the acceleration of
an electron in a uniform electric field that has a magnitude of 100
N/C?
(c) Compute the time it takes for an electron placed at rest in a
uniform electric field that has a magnitude of 100 N/C to reach a
speed 0.01c. (When the speed of an electron approaches the
speed of light c, relativistic kinematics must be used to calculate
its motion, but at speeds of 0.01c or less, nonrelativistic
kinematics is sufficiently accurate for most purposes.)
(d) How far does the electron travel in that time?
Solution:
Tipler 22.P.013
A uniform line charge that has a linear charge density λ = 3.5
nC/m is on the x axis between x = 0 to x = 5.0 m.
(a) What is its total charge?
(b) Find the electric field on the x axis at x = 6.0 m.
(c) Find the electric field on the x axis at x = 9.0 m.
(d) Find the electric field on the x axis at x = 250 m.
(e) Estimate the electric field at x = 250 m, using the
approximation that the charge is a point charge on the x axis at x
= 2.5 m.
(f) Compare your result with the result calculated in part (d) by
finding the ratio of the approximation to the exact result. To do
this, you will need to assume that the values given in this
problem statement are valid to more than two significant figures.
Solution:
Tipler 22.P.015
A charge of 2.75 µC is uniformly distributed on a ring of radius
8.5 cm. Find the electric field strength on the axis at the
following locations.
(a) 1.2 cm from the center of the ring
(b) 3.6 cm from the center of the ring
(c) 4.0 m from the center of the ring
(d) Find the field strength at 4.0 m using the approximation that
the ring is a point charge at the origin.
(e) Compare your results for parts (c) and (d) by finding the ratio
of the approximation to the exact result.
Solution:
Tipler 22.P.029
An electric field is = 300 N/C i for x > 0, 0 if x = 0 and E = -300
N/C i for x < 0. A cylinder of length 20 cm and radius 4.0 cm has
its center at the origin and its axis along the x axis such that one
end is at x = +10 cm and the other is at x = -10 cm.
(a) What is the flux through each end?
(b) What is the flux through the curved surface of the cylinder?
(c) What is the net outward flux through the entire cylindrical
surface?
(d) What is the net charge inside the cylinder?
Solution:
Tipler 22.P.032
What is the electric flux through one side of a cube that has a
single point charge of -3.00 µC placed at its center? Hint: You do
not need to integrate any equations to get the answer.
Solution:
Problems for Practice
Tipler 21.P.012
Four charges are fixed in place at the corners of a square as
shown below. No other charges are nearby. Which of the
following statements is true?
(a) E is zero midway between the top two charges and midway
between the bottom two charges
(b) E is zero at the center of the square
(c) E is zero at the midpoints of all four sides of the square
Solution:
(b) At the center of the square the 2 positive charges alone
produce a net E-field of zero, as well as the 2 negative charges.
Thus, the net force acting on a test charge at the midpoint of the
square is zero.
Tipler 21.P.027
Three point charges are on the x axis: q1 = -6.0 µC is at x = -3.0
m, q2 = 4.0 µC is at the origin, and q3 = -6.0 µC is at x = 3.0 m.
Find the force on q1.
Solution:
Tipler 22.P.016
A nonconducting disk of radius R lies in the z = 0 plane with its
center at the origin. The disk has a uniform surface charge
density σ. Find the value of z for which Ez = σ/(4ε0). Note that at
this distance, the magnitude of the electric field strength is half
the electric field strength at points on the z axis that are very
close to the disk. (Use R as necessary.)
Solution: