Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 10th + WebAssign Printed Access Card for Serway/Jewett's Physics for Scientists and Engineers, 10th, Multi-Term
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ISBN: 9781337888592
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Chapter 31, Problem 42AP
You are working on an LC circuit for an experiment you are performing in your basement. You have an appropriate capacitor, but you need to build your own inductor. You wish to cut a wooden ring with a rectangular cross section, as shown in Figure P31.41, from wood with thickness h. You want to wrap N turns of wire around it to form a toroidal inductor. For your experiment, you need to have energy UB stored in the inductor when it carries a current i. In order to cut the appropriate wooden ring, you need to determine the ratio b/a. Ignore any effect of the wood core on the magnetic field.
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Given the LC circuit above, with L =
The switch is closed at time t = 0.
50mH, C = 5µF, Qo= 3 x 10-³ C.
a. Find the capacitor's charge at t = 3ms.
b. What are the capacitor's and inductor's energy at that time?
2. A square copper frame has sides of length b. A very long thin solenoid goes through
the frame as shown. The solenoid has N tums in a total length H and radius a.
Assume that > > 2a so the solenoid goes through the frame. The solenoid has an
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frequency w is constant.
a. Write an expression for the magnetic flux through the square frame as a
function of time. Hint: what is the magnetic field inside and outside a long
solenoid?
b. Determine the EMF induced in the frame as a function of time. Please use
Faraday's Law with the minus sign.
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c. What is the amplitude of the induced EMF? The amplitude of a sinusoidal function is the maximum deviation of
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d. What is the induced EMF as a function of time if the square frame was small enough to fit entirely inside the
solenoid (> <2a)…
2. A square copper frame has sides of length b. A very long thin solenoid goes through
the frame as shown. The solenoid has N turns in a total length H and radius a.
Assume that b> 2a so the solenoid goes through the frame. The solenoid has an
AC current given by I(t) = I, sin(wt) with ccw counted as positive. The angular
frequency w is constant.
C.
a.
b. Determine the EMF induced in the frame as a function of time. Please use
Faraday's Law with the minus sign.
d.
Write an expression for the magnetic flux through the square frame as a
function of time. Hint: what is the magnetic field inside and outside a long
solenoid?
ON
2a
head on view
b
What is the amplitude of the induced EMF? The amplitude of a sinusoidal function is the maximum deviation of
the function from the average value. Hint: what is the largest value that cosine or sine can have during a cycle?
What is the induced EMF as a function of time if the square frame was small enough to fit entirely inside the
solenoid (b<2a) as…
Chapter 31 Solutions
Bundle: Physics for Scientists and Engineers with Modern Physics, Loose-leaf Version, 10th + WebAssign Printed Access Card for Serway/Jewett's Physics for Scientists and Engineers, 10th, Multi-Term
Ch. 31.1 - A coil with zero resistance has its ends labeled a...Ch. 31.2 - Prob. 31.2QQCh. 31.3 - Prob. 31.3QQCh. 31.4 - Prob. 31.4QQCh. 31.5 - (i) At an instant of time during the oscillations...Ch. 31 - Prob. 1PCh. 31 - Prob. 2PCh. 31 - An emf of 24.0 mV Ls induced in a 500-turn coil...Ch. 31 - Prob. 4PCh. 31 - Prob. 5P
Ch. 31 - A toroid has a major radius R and a minor radius r...Ch. 31 - Prob. 7PCh. 31 - Prob. 8PCh. 31 - Prob. 9PCh. 31 - Prob. 10PCh. 31 - Prob. 11PCh. 31 - Show that i = Iiet/ is a solution of the...Ch. 31 - Prob. 13PCh. 31 - You are working as a demonstration assistant for a...Ch. 31 - Prob. 15PCh. 31 - The switch in Figure P31.15 is open for t 0 and...Ch. 31 - Prob. 17PCh. 31 - Two ideal inductors, L1 and L2, have zero internal...Ch. 31 - Prob. 19PCh. 31 - Prob. 20PCh. 31 - Prob. 21PCh. 31 - Complete the calculation in Example 31.3 by...Ch. 31 - Prob. 23PCh. 31 - A flat coil of wire has an inductance of 40.0 mH...Ch. 31 - Prob. 25PCh. 31 - Prob. 26PCh. 31 - Prob. 27PCh. 31 - Prob. 28PCh. 31 - In the circuit of Figure P31.29, the battery emf...Ch. 31 - Prob. 30PCh. 31 - An LC circuit consists of a 20.0-mH inductor and a...Ch. 31 - Prob. 32PCh. 31 - In Figure 31.15, let R = 7.60 , L = 2.20 mH, and C...Ch. 31 - Prob. 34PCh. 31 - Electrical oscillations are initiated in a series...Ch. 31 - Review. Consider a capacitor with vacuum between...Ch. 31 - A capacitor in a series LC circuit has an initial...Ch. 31 - Prob. 38APCh. 31 - Prob. 39APCh. 31 - At the moment t = 0, a 24.0-V battery is connected...Ch. 31 - Prob. 41APCh. 31 - You are working on an LC circuit for an experiment...Ch. 31 - Prob. 43APCh. 31 - Prob. 44APCh. 31 - Prob. 45APCh. 31 - At t = 0, the open switch in Figure P31.46 is...Ch. 31 - Review. The use of superconductors has been...Ch. 31 - Review. A fundamental property of a type 1...Ch. 31 - Prob. 49APCh. 31 - In earlier times when many households received...Ch. 31 - Assume the magnitude of the magnetic field outside...Ch. 31 - Prob. 52CPCh. 31 - Prob. 53CP
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