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1308 E&M
Reviews for the final exam
Charge conservation:
The Sun generates most of its light through a series of nuclear reactions
called the proton-proton chain. The overall process of these nuclear
reactions can be summarized as 4 1H → 2He + 2ν + 2γ + 2? where ν is a
small neutral particle called a neutrino, and γ is a photon (a particle of
light), which is also neutral. The pre-subscripts on the element symbols
H (hydrogen) and He (helium) indicate the number of protons in the
nucleus of each element. What is the charge of the unknown entity "?" ?
Charge induction:
You are locked in a rubber room and given a pair of rubber gloves along
with a positively charged bar of gold (marked with a "+") and two
electrically neutral bars of gold. You will be released if you can produce a
negatively charged bar of gold, and you get to keep the gold. Explain how
you might accomplish this
1308 E&M
Coulomb’s Law of electrostatic forces
Coulomb’s Law + friction concept:
Two 2.0 kg plastic garbage cans are sitting 2.6 meters apart on a sticky
classroom floor (coefficient of static friction μs = 0.40). They are not
moving. If the first one has a charge of 10 μC, find (a) the most negative
possible charge and (b) the most positive possible charge for the other
garbage can. Assume that the charges can be represented as point
charges located at the cans' centers.
Use the concept of symmetry:
A bicycle wheel with radius 35 cm has 73 charges (1.0 μC each) spaced at
regular intervals along its edge. A flea with charge −0.010 μC lands in the
center of the wheel. (a) What is the net electric force on the flea? (b)
One of the charges is removed. Find the magnitude of the new net
electric force on the flea.
1308 E&M
Coulomb’s Law of electrostatic forces
Coulomb’s law + other physics concepts:
Two 0.600 kg oppositely charged basketballs are following a clockwise
circular path on a frictionless, freshly waxed basketball court. The balls are
on opposite sides of the circle at all times, and are 10.0 m apart. Their
charges cause the balls to continue on the circular path at a speed of
1.20 m/s. (a) Determine the product of the charges on the basketballs. (b)
Now assume the charge on the positively charged ball is twice the
magnitude of the negatively charged one. Determine the charge on the
negative ball. (c) Determine the charge on the positive ball. (d) The same
basketballs are now 5.00 m apart, but they are still moving in a circular
path. Determine their speed. (e) One of the basketballs now has a mass of
only 0.550 kg. Is it still possible for the two balls to hold each other so
that they travel along identical circular paths? Explain your answer.
1308 E&M
Electric field
1.
Three locations, 1, 2, and 3, are labeled in the electric field diagram. At
which of these locations is the strength of the field the greatest?
2.
In the diagram, two charges of +2q and −5q are placed on a line. (a) There
is a point on the line where the strength of the electric field due to the
two charges is zero. Describe where the point is, relative to the positions
of the two charges. (b) Is there any point not on the line, where the
strength of the electric field is zero?
1308 E&M
1.
Electric field and Gauss’s law
A solid conducting sphere with a radius of 35.4 cm contains a total charge
of 5.46 mC, evenly distributed over its surface. (a) What is the direction
of the electric field at its surface? (b) What is the strength of the
electric field at its surface?
1308 E&M
Electric potential
1.
The gravitational potential energy of all the water stored behind a very
large dam is 1.2×1016 J, using the base of the dam as the reference point
for zero PE. Imagine you could store the same amount of potential energy
in a system consisting of two particles, each with a charge of 0.0020 C.
How far apart should you place the charges? (3.0e−12 m)
2.
Two infinitesimally small point charges of +2.0 μC each are initially
stationary and 5.0 m apart. (a) How much work is required to bring them to
a stationary position 2.0 m apart? (b) 2.0 mm apart? (c) With a finite
amount of energy, is it possible to push them together?
3.
A charge of +3.00 μC is placed at the point (0 m, 0 m, 0 m); a charge of
−4.50 μC is placed at the point (2.00 m, −5.00 m, 7.00 m); finally, a charge
of −1.00 μC is placed at the point (1.00 m, 1.00 m, 1.00 m). (a) What is the
electric potential energy of this configuration? (b) If a neutron (a particle
with the mass of the proton but no electric charge) is brought in from
infinity and placed at the point (−3.00 m, 2.00 m, 5.50 m), how does the
electric potential energy of the configuration change? ((a) −2.46e−2 J (b) It
stays the same )
1308 E&M
Electric potential
1.
A certain 4.8-volt cellular telephone battery has a capacity of 600 mAh.
(One mAh equals 3.6 coulombs.) When the battery's charge is too low to
run the phone any longer (assume it is zero), the battery must be
recharged. (a) How much work is done by the recharger? (b) If electricity
costs you 9.0 cents per kWh, how much does one recharge cost you?
((a) 1.04e4 J (b) $ 2.6e−4 )
2.
In the diagram you see the spark gap between the contacts of an
automobile spark plug. When the contacts are charged to a potential
difference great enough to cause a spark to jump across the gap, the
electric field between them approximates a uniform field of strength
3.1×106 N/C. What is the magnitude of the potential difference that
causes the spark? (710 V)
1308 E&M
Gauss’s Law
1.
A cube with 1 m edges is in a uniform electric field of magnitude 17 N/C.
The electric field intersects the top of the cube at a 30° angle to the
normal, and is parallel to two faces of the cube. The area vector for each
face of the cube points outward. (a) What is the relationship between the
electric flux through the top face and the electric flux through the
bottom face? (b) Calculate the net electric flux through the entire surface
of the cube. ((a) They have equal magnitude but opposite signs (b) 0 (N/C)·m2)
2.
A vertical, infinite, nonconducting plane has uniform positive charge. A
weightless thread is attached to the plane, and at the end of the thread
there is a small spherical ball with a charge of +78.6 μC, and a mass of
0.954 kg. The angle that the thread makes with the plane is 37.3°. What is
the charge density σ of the plane?
1308 E&M
1.
Gauss’s Law
Consider a rectangular slab, infinite in length and width and extending a
distance h/2 on either side of the yz plane, so that it has a finite
thickness h. The slab has a constant positive charge density ρ. (a) In what
direction does the electric field point for positive x? (b) In what direction
does the electric field point for negative x? (c) Determine the electric
field inside the slab, for 0 < x < h/2, using Gauss' Law. (d) Determine the
electric field outside the slab, for x > h/2, using Gauss' Law.
((a) In the positive x direction. (b) In the negative x direction. (c) ρx/ε0 (d) ρh/2ε0 )
1308 E&M
Direct current, resistance
1.
Two like charges of one coulomb each, separated by one meter, repel each
other with a force of 8.99×109 N, equivalent to the weight of 10
battleships. A flashlight bulb may have a current of 0.40 A flowing through
it, which is equivalent to one coulomb of charge flowing through every 2.5
seconds. But a flashlight circuit is clearly not subject to tremendous
electrostatic forces – or even small ones. Why not?
2.
Two wires are connected to a conducting sphere of radius 7.75 cm, which is
initially uncharged. One wire carries a current of 3.47 μA into the sphere,
and another wire carries a current of 1.26 μA out of the sphere. How long
does it take to to produce an electric potential of 5.00 MV at a distance of
11.6 cm away from the center of the sphere?
3.
The graphite in a pencil has a resistivity of 7.84×10−6 Ωm. The graphite's
diameter is 0.700 mm and its length is 40.0 mm. (a) Find the resistance of
this graphite "wire." (b) Find the diameter of a cylindrical copper wire of
the same length (having resistivity 1.70×10−8 Ωm) that would produce the
same resistance.