AP PHYSICS C
NAME_____________________
CH. 21 ELECTRIC FORCES & FIELDS
DATE_____________________
SAMPLE PROBLEMS:
1. Refer to the picture below. Apply Newton’s second law of motion and Coulomb’s law to verify
the forces that are given.
2.
An electrically neutral penny, of mass 3.11 g, contains equal amounts of positive and negative
charge. Assuming the penny is made entirely of copper, what is the magnitude q of the total
positive (or negative charge) charge in the penny?
3.
The average distance between the electron and the central proton in the hydrogen atom is 5.3
x 10-11 m.
a. What is the magnitude of the average electrostatic force that acts between these two
particles?
b. What is the magnitude of the average gravitational force that acts between these
particles?
4. After viewing the simulation at
http://phet.colorado.edu/simulations/sims.php?sim=Charges_and_Fields , how is the electric
field vector drawn due to a positive point charge and a negative point charge?
5.
Sketch the electric field for each of the following:
a. Positive point charge
b. Negative point charge
c. Two positive point charges
d. One positive point charge and
one negative point charge
e. Two negative point charges
f.
Oppositedly charged parallel
plates
6. The diagram below shows a charge +8q at the origin of an x-axis and a charge of -2q at x = L. At
which points is the net electric field due to these two charges zero?
+8q
-2q
L
7.
The nucleus of a uranium atom has a radius R of 6.8 fm. Assuming that the positive charge of
the nucleus is distributed uniformly, determine the electric field at a point on the surface of the
nucleus due to that charge. (Note: 1 fm = 1 x 10-15 m; The atomic mass unit for uranium is 92.)
8.
Electric Field due to a continuous distribution of charge:
𝜆=
𝑑𝑞
𝑑𝑠
𝑑𝑞
𝜎 = 𝑑𝐴
𝑑𝑞
𝜌 = 𝑑𝑉
9.
Charge per unit length—linear density.
Charge per unit surface area
Charge per unit volume
Through the use of integration, determine the total electric field at a point that is x from the
center of a continuous ring of positive charge, Q, that has a radius of R.
10. A plastic rod having a uniformly distributed charge of –Q. The rod has been bent in a 120o
circular arc of radius r. The coordinate axes are placed such that the axis of symmetry of the rod
lies along the x-axis and the origin is at the center of curvature of the rod. In terms of Q and r,
what is the electric field due to the rod at the origin of the axes?
11. In the Millikan’s oil-drop apparatus, a drop of radius 2.76 μm has an excess charge of three
electrons. What are the magnitude and direction of the electric field that is required to balance
the drop so it remains stationary in the apparatus? The density of the oil is 920 kg/m3.
12. Determine the path that the proton will follow.
If the proton is entering the electric field of 10 N/C at the positive plate, how far does it move
vertically if the plates are 10 cm long?
13. An electric dipole has been placed in a uniform electric field, E.
a.
What is the net force acting on the dipole?
b. What is the net torque about the center of the rod?
c. What is the definition of the dipole moment?
d. How is the direction of the electric dipole determined?
e. The potential energy of an electric dipole is associated with the
_______________________________________________________________________.
f.
The dipole is at its lowest potential energy when it is in its equilibrium orientation,
which is when its moment p is _________________with the E-field and the torque is
zero. This position is called ________________________________________________.
g. Its greatest potential energy is when p is __________________to the E-field. This is
called ______________________________________________.
h. How do you determine the work done by the external field on the diplole?
i.
How is the potential energy defined?
14. A neutral water molecule in its vapor state has an electric dipole moment of 6.2 x 10-30 C-m.
a. How far apart are the molecule’s centers of positive and negative charge?
b. If the molecule is placed in an electric field of 1.5 x 104 N/C, what maximum torque can
the field exert on it?
c. How much work must an external agent do to turn this molecule end for end in this
field, starting from its fully aligned position, for which θ = 0?