Download The following videos will help prepare you with concepts and

The following videos will help prepare you with concepts and images for our study of fields
this spring. The link to Mechanical Universe will get you to the list of episodes
11. Gravity, Electricity, Magnetism
Shedding light on the mathematical form of the gravitational, electric, and magnetic forces.
28. Static Electricity
Eighteenth-century electricians knew how to spark the interest of an audience with the principles
of static electricity.
29. The Electric Field
Faraday's vision of lines of constant force in space laid the foundation for the modern force field
theory.
30. Potential and Capacitance
Franklin proposes a successful theory of the Leyden jar and invents the parallel plate capacitor.
31. Voltage, Energy, and Force
When is electricity dangerous or benign, spectacular or useful?
35. The Magnetic Field
The law of Biot and Sarvart, the force between electric currents, and Ampère's law.
36. Vector Fields and Hydrodynamics
Force fields have definite properties of their own suitable for scientific study.
On the pages that follow, there are a set of conceptual study questions. I won’t be
grading your responses, but I will construct the multiple choice questions on the exam
from these.
In the questions below, all conductors are perfect conductors with zero resistance, all
insulators have infinite resistance and the direction of the electric field is the direction of
the force on a positive test charge.
A) A charge of +Q is located at the origin and a second charge of +Q is located at x= 2 cm. The
force between them is F.
1) When the charge at +2cm is replaced with a charge of +4Q, what is the force exerted on it
by the charge at the origin?
2) What is the force exerted on the charge at the origin by the +4Q charge?
3) If the +4Q charge is replaced with a +3Q charge at x = 4cm, what is the force exerted on it
by the charge at the origin?
4) The charge at the origin is replaced by a charge of -2Q, what is the force exerted on it by
the +3Q charge at x = 4cm?
B) Below are two sets of electric equipotentials labeled with the voltage values for each.
1) Rank the locations A, B, C and D in order of increasing electric field strength.
2) What would be the direction and relative magnitude of the force on a charge of +1
Coulomb placed at A, B, C and D?
3) What are the relative potential energies of a +1 Coulomb charge placed at A, B, C and
D?
C) A number of positive charges are placed at one place on a hollow conducting sphere.
1) After a few minutes, where are the charges located?
2) What is the value of the electric field inside the conductor?
3) Would the electric field be different if the conductor was solid?
4) If the charges were placed on an insulating sphere, where would they be after a few
minutes?
D) In the late 1700’s, a raging debate concerning the optimum shape of the end of a lightning
rod existed between Benjamin Franklin and the British scientific establishment. Consider a
conductor in the shape of a cone with
a hemisphere at its base:
If many negative charges are
deposited on the surface, how will
they be distributed?
Consider a spot on the hemisphere
and the point of the cone; What
direction are the forces between
charges at such locations? When the
forces are balanced, what is the
charge density like at these two spots?
E) Two electrons, A and B enter a uniform electric field at different times, each at initial velocity
v; one (B) parallel to the equipotentials and the second (A) perpendicular to them. Describe the
paths they take as they move through the field.
F) Describe the ways in which gravity fields, electric fields and magnetic fields differ.
G) For the charges in the figure below, draw enough electric field lines to show the general
shape of the field.
H) For the charged conductors in the diagram below, draw in enough equipotentials to show
the shape of the field. [4 points].
I) A capacitor has a charge +Q on one plate and –Q on the other.
(1) If the charge on a capacitor is doubled, what does that do to the voltage across it? How
much does the energy stored in the capacitor change?
(2) Suppose the voltage across a capacitor were doubled, what happens to the charge and
the energy?
(3) What happens if the dielectric constant of the insulator between the plates is doubled?
What is the new voltage and energy for the capacitor?
Magnetic fields
(J) Which of the following will NOT induce a potential in a conducting loop in a magnetic field?
(a) The strength of the magnetic field is changed.
(b) The loop is rotated about an axis perpendicular to the magnetic field.
(c) A very strong magnet is in the center of a conducting loop, at rest.
(d) The size of the loop is changed.
(K) Magnetic field lines
(a) end on magnetic poles.
(b) trail behind moving charges.
(c) are always perpendicular to electric field lines. (d) close without ending.
(L) You are given two iron bars which are identical in appearance and told one of them is a
weak magnet. Using only the two bars and one trial, how do you determine which one is the
magnet?
(M) A magnetic field exerts a force on which of the following?
(a) a current carrying wire
(b) a magnet
(c) a moving electric charge
(d) a stationary electric charge
(N) Describe the magnetic field produced by
(1) a wire
(2) a circular loop
(3) a solenoid
(4) a toroid
(O) A charged particle moving at velocity v enters a uniform magnetic field moving
perpendicular to the field lines.
1) Describe its motion.
2) What would change if the velocity doubled?
3) What if the mass were doubled?
4) What is the field strength were doubled?
5) What if the particle was moving parallel to the field lines?
(P) Two very long wires carry currents of 1 amp. Describe the force between them when the
currents are (1) perpendicular, (2) in the same direction, (3) in opposite directions.
(4) Current is passed through a spring, does it stretch or contract?