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A rectangular toroid with inner radius R 1 = 7.0 cm, outer radius R 2 = 9.0 cm , height h = 3.0 , and N = 3000 turns is filled with an iron core of magnetic susceptibility 5.2 × 10 3 . (a) What is the self-inductance of the toroid? (b) If the current through the toroid is 2.0 A, what is the magnetic field at the center of the core? (c) For this same 2.0-A current, what is the effective surface current formed by the aligned atomic current loops in the iron core?

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The switch S of the circuit shown below is closed at t = 0 . Determine (a) the initial current through the battery and (b) the steady-state current through the battery.

A 12 volt battery is connected in series with a 5 ohm resistor, a 1 Henry inductor, a 3 ohm resistor and an open switch S. Parallel to the 3 ohm resistor is a 2 Henry inductor.

a. 0 A; b. 2.4 A

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In an oscillating RLC circuit, R = 7.0 Ω , L = 10 mH , and C = 3.0 μ F . Initially, the capacitor has a charge of 8.0 μ C and the current is zero. Calculate the charge on the capacitor (a) five cycles later and (b) 50 cycles later.

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A 25.0-H inductor has 100 A of current turned off in 1.00 ms. (a) What voltage is induced to oppose this? (b) What is unreasonable about this result? (c) Which assumption or premise is responsible?

a. 2.50 × 10 6 V ; (b) The voltage is so extremely high that arcing would occur and the current would not be reduced so rapidly. (c) It is not reasonable to shut off such a large current in such a large inductor in such an extremely short time.

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Challenge problems

A coaxial cable has an inner conductor of radius a, and outer thin cylindrical shell of radius b. A current I flows in the inner conductor and returns in the outer conductor. The self-inductance of the structure will depend on how the current in the inner cylinder tends to be distributed. Investigate the following two extreme cases. (a) Let current in the inner conductor be distributed only on the surface and find the self-inductance. (b) Let current in the inner cylinder be distributed uniformly over its cross-section and find the self-inductance. Compare with your results in (a).

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In a damped oscillating circuit the energy is dissipated in the resistor. The Q -factor is a measure of the persistence of the oscillator against the dissipative loss. (a) Prove that for a lightly damped circuit the energy, U , in the circuit decreases according to the following equation.

d U d t = −2 β U , where β = R 2 L .

(b) Using the definition of the Q -factor as energy divided by the loss over the next cycle, prove that Q -factor of a lightly damped oscillator as defined in this problem is

Q U begin Δ U one cycle = 1 R L C .

( Hint: For (b), to obtain Q , divide E at the beginning of one cycle by the change Δ E over the next cycle.)


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The switch in the circuit shown below is closed at t = 0 s . Find currents through (a) R 1 , (b) R 2 , and (c) the battery as function of time.

A 12 volt battery is connected to a 6 ohm resistor and a switch S, which is open at time t=0. Connected in parallel with the 6 ohm resistor are another 6 ohm resistor and a 24 Henry inductor.
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A square loop of side 2 cm is placed 1 cm from a long wire carrying a current that varies with time at a constant rate of 3 A/s as shown below. (a) Use Ampère’s law and find the magnetic field as a function of time from the current in the wire. (b) Determine the magnetic flux through the loop. (c) If the loop has a resistance of 3 Ω , how much induced current flows in the loop?

a. d B d t = 6 × 10 −6 T/s; b. Φ = μ 0 a I 2 π ln ( a + b b ) ; c. 4.0 nA

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A rectangular copper ring, of mass 100 g and resistance 0.2 Ω , is in a region of uniform magnetic field that is perpendicular to the area enclosed by the ring and horizontal to Earth’s surface. The ring is let go from rest when it is at the edge of the nonzero magnetic field region (see below). (a) Find its speed when the ring just exits the region of uniform magnetic field. (b) If it was let go at t = 0 , what is the time when it exits the region of magnetic field for the following values: a = 25 cm , b = 50 cm , B = 3 T , and g = 9.8 m/s 2 ? Assume the magnetic field of the induced current is negligible compared to 3 T.

Figure a shows a box with crosses in it. It is labeled t=0. An area within it is demarcated with breadth equal to a and length equal to b. Figure b shows the same box with crosses in it. It is labeled, “when ring exits”. The demarcated are from figure a is now below the box. There are two downward arrows labeled g and v.
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Questions & Answers

Using Kirchhoff's rules, when choosing your loops, can you choose a loop that doesn't have a voltage?
Michael Reply
how was the check your understand 12.7 solved?
Bysteria Reply
LOAK Reply
he's the father of 3 newton law
he is Chris Issaac's father :)
how to name covalent bond
Bryan Reply
what do you understand by the drift voltage
Brunelle Reply
what do you understand by drift velocity
well when you apply a small electric field to a conductor that causes to add a little velocity to charged particle than usual, which become their average speed, that is what we call a drift.
drift velocity
what is an electromotive force?
Danilo Reply
It is the amount of other forms of energy converted into electrical energy per unit charge that flow through it.
How electromotive force is differentiated from the terminal voltage?
in the emf power is generated while in the terminal pd power is lost.
what is then chemical name of NaCl
Sagar Reply
sodium chloride
sodium chloride
How can we differentiate between static point and test charge?
Comfort Reply
Wat is coplanar in physics
Humble Reply
two point charges +30c and +10c are separated by a distance of 80cm,compute the electric intensity and force on a +5×10^-6c charge place midway between the charges
Tijani Reply
what is the difference between temperature and heat
Ishom Reply
Heat is the condition or quality of being hot While Temperature is ameasure of cold or heat, often measurable with a thermometer
Temperature is the one of heat indicators of materials that can be measured with thermometers, and Heat is the quantity of calor content in material that can be measured with calorimetry.
the average kinetic energy of molecules is called temperature. heat is the method or mode to transfer energy to molecules of an object but randomly, while work is the method to transfer energy to molecules in such manner that every molecules get moved in one direction.
2. A brass rod of length 50cm and diameter 3mm is joined to a steel rod of the same length and diameter. What is the change in length of the combined rod at 250°c( degree Celsius) if the original length are 40°c(degree Celsius) is there at thermal stress developed at the junction? The end of the rod are free to expand (coefficient of linear expansion of brass = 2.0×10^-5, steel=1.2×10^-5k^1)
A charge insulator can be discharged by passing it just above a flame. Explain.
Mudassar Reply
of the three vectors in the equation F=qv×b which pairs are always at right angles?
what is an ideal gas?
Justine Reply
What is meant by zero Kelvin ?
Why does water cool when put in the pot ?
when we pour the water in a vessel(pot) the hot body(water) loses its heat to the surrounding in order to maintain thermal equilibrium.Thus,water cools.
when we drop water in the pot, the pot body loses heat to surrounded in order to maintain thermal equilibrium thus,water cool.
my personal opinion ideal gas means doesn't exist any gas that obey all rules that is made for gases, like when get the temp of a gas lower, it's volume decreases.since the gas will convert to liquid when the temp get lowest.. so you can imagine it, but you can't get a gas at the lowest T
Edit An ideal gas is a theoretically gascomposed of many randomly moving point particles whose only interactions are perfectly elastic collisions.
ideal gases are real gases at low temperature
Practice Key Terms 1

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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