Download Problem Set 10

Problem Set 10
Due: 12/1/10, Wednesday
Chapter 30: Induction & Inductance
Exercises & Problems: 1, 17, 19, 35, 41, 45, 80
Chapter 30 Even Answers
31 mV, -0.011 V; 5500 V; 0.0295 C; 60.0 mV, 60.0 mA, 14.4 μW, 28.7 nN, 14.4
μW ; 2.45 mWb, 64.5 mH; decrease, 68.0 mH; 120, 0.600 mH;
******EXAM 2 Alert******
December 1, Wednesday
Question A
A car stops for a red light at an intersection. As it comes to a halt, it moves over a coil
embedded in the surface of the road. As a result, the light soon changes from red to
green. Explain how the coil is able to signal the light to change.
Question B
A farmer claimed that the high-voltage transmission lines running parallel to his fence
induced dangerously large voltages on the fence. Is this with the realm of possibility?
Explain. (The lines carry alternating current that changes direction 120 times each
second.)
Question C
Some modern stove burners are based on induction. That is, an ac current passes
around a coil that is the “burner,” a burner that never gets hot. Explain why it will heat a
metal pan but not a glass container.
Question D
A region where no magnetic field is desired is surrounded by a sheet of low-resistivity
metal. (a) Will this sheet shield the interior from a rapidly changing magnetic field
outside? Explain. (b) Will it act as a shield to a static magnetic field? (c) What if the sheet
is superconducting (resistivity = 0)?
Problem 30.1
In Fig. 30-37, the magnetic flux through the loop increases accord ing to
the relation B = 6.0t2 + 7.0t, where B is in mWb and t is in seconds. (a)
What is the magnitude of the emf induced in the loop when t = 2.0 s? (b)
Is the direction of the current through R to the right or left?
Problem 30.17
An electric generator contains a coil of 100 turns of wire, each forming a rectangular loop
50.0 cm by 30.0 cm. The coil is placed entirely in a uniform magnetic field with
magnitude B = 3.50 T and with B initially perpendicular to the coil's plane. What is the
maximum value of the emf produced when the coil is spun at 1000 rev/min about an axis
perpendicular to B?
Problem 30.19
One hundred turns of (insulated) copper wire are wrapped around a wooden cylindrical
core of cross-sectional area 1.20  103 m2. The two ends of the wire are connected to a
resistor. The total resistance in the circuit is 13.0 Ω. If an externally applied uniform
longitudinal magnetic field in the core changes from 1.60 T in one direction to 1.60 T in
the opposite direction, how much charge flows through a point in the circuit during the
change?
Problem 30.35
Figure 30-59 shows a rod of length L = 10.0 cm that is forced to move
at constant speed v = 5.00 m/s along horizontal rails. The rod, rails,
and connecting strip at the right form a conducting loop. The rod has
resistance 0.400 Ω; the rest of the loop has negligible resistance. A
current i = 100 A through the long straight wire at distance a = 10.0
mm from the loop sets up a (nonuniform) magnetic field through the
loop. Find the (a) emf and (b) current induced in the loop. (c) At what
rate is thermal energy generated in the rod? (d) What is the
magnitude of the force that must be applied to the rod to make it
move at constant speed? (e) At what rate does this force do work on
the rod?
Problem 30.41
A circular coil has a 10.0 cm radius and consists of 30.0 closely wound turns of wire. An
externally produced magnetic field of magnitude 2.60 mT is perpendicular to the coil. (a)
If no current is in the coil, what magnetic flux links its turns? (b) When the current in the
coil is 3.80 A in a certain direction, the net flux through the coil is found to vanish. What
is the inductance of the coil?
Problem 30.45
At a given instant the current and self-induced emf in an inductor are
directed as indicated in the figure. (a) Is the current increasing or
decreasing? (b) The induced emf is 17 V, and the rate of change of
the current is 25 kA/s; find the inductance.
Problem 30.80
The inductance of a closely wound coil is such that an emf of 3.00 mV is induced when
the current changes at the rate of 5.00 A/s. A steady current of 8.00 A produces a
magnetic flux of 40.0 μWb through each turn. (a) Calculate the inductance of the coil. (b)
How many turns does the coil have?