Physics for Scientists and Engineers
10th Edition
ISBN: 9781337553278
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Question
Chapter 31, Problem 28P
(a)
To determine
To show: mutual induction of pair of two single turn circular loop of wire is
(b)
To determine
The value of mutual inductance M
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Two single-turn circular loops of wire have radii R and r, with R >> r. The loops lie in the same plane and are concentric. (a) Show that the mutual inductance of the pair is approximately M = μ0πr2/2R. (b) Evaluate M for r = 2.00 cm and R = 20.0 cm.
A rectangular conducting loop is placed on a flat surface, with the longer sides parallel to a current-carrying wire on the same surface, as shown in the figure.
Assume h = 0.500 mm, w = 1.40 mm, and e = 2.50 mm. What is the mutual inductance (in pH) for this configuration?
pH
A rectangular loop of N closely packed turns is positionednear a long straight wire .What is the mutual inductanceMforthe loop–wire combinationif N= 100, a= 1.0 cm, b =8.0 cm, and l =30 cm?
Chapter 31 Solutions
Physics for Scientists and Engineers
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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- Suppose that a rectangular toroid has 2000 windings and a self-inductance of 0.040 H. If h = 0.10 m, what is the ratio of its outer radius to its inner radius?arrow_forwardShow that N m /l and el(dl/dt), which are both expressions for se1f-inductance, have the same units.arrow_forwardA long, cylindrical solenoid with 100 turns per centimeter has a radius of 1.5 cm. (a) Neglecting end effects, that is the self-inductance per unit length of the solenoid? (b) If the current through the solenoid changes at the rate 5.0 AJs, what is the emf induced per unit length?arrow_forward
- In an oscillating LC circuit the maximum charge on the capacitor is 2.0 × 10-6 C and the maximum current through the inductor is 8.0 mA. (a) What is the period of the oscillations? (b) How much time elapses between an instant when the capacitor is uncharged and the next instant when it is fully charged?arrow_forwardThe self-inductance and capacitance of an LC circuit e 0.20 mH and 5.0 pF. What is the angular frequency at which the circuit oscillates?arrow_forwardAt s1iat frequency is the reactance of a 20F capacitor equal to that of a 10-mH inductor?arrow_forward
- A 5000-pF capacitor is charged to 100 V and then quickly connected to an 80-mH inductor. Determine (a) the maximum energy stored in the magnetic field of the inductor, (b) the peak value of the current, and (c) the frequency of oscillation of the circuit.arrow_forwardA rectangular wire loop with length a and width b lies in the xy-plane, as shownbelow. Within the loop there is a time-dependent magnetic field given by B(t)=C((xcost)i+(ysint)k) ,with B(t) intesla. Determine the emf induced in the loop as a function of time.arrow_forwardSuppose that a cylindrical solenoid is wrapped around a core of iron whose magnetic susceptibility is x. Using Equation 14.9, show that the self-inductance of the solenoid is given by L=(l+x)+0n2Al where l is its length, A its cross-sectional area and N its total number of turns. Nm=Uarrow_forward
- The self-inductance and capacitance of an oscillating LC circuit are L = 20 mH and C = 1.0 F , respectively. (a) What is the frequency of the oscillation? (b) If the maximum potential difference the plates of the capacitor is 50 V, what is the maximum current in the circuit?arrow_forwardA steady current flows through a circuit with a large induct3ve time constant. When a switch in the circuit is opened, a large spark across the terminals of the switch. Explain.arrow_forwardA solenoid with 4 x 107turns/m has an iron core placed in it whose magnetic susceptibility is 4.0 x 103. (a) If a cent of 2.0 A flows through the solenoid, what is the magnetic field in the iron core? (b) What is the effective surface current formed by the aligned atomic current loops in the iron core? (c) What is the self-inductance of the filled solenoid?arrow_forward
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