University Physics (14th Edition)
14th Edition
ISBN: 9780133969290
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
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Question
Chapter 30, Problem Q30.4DQ
To determine
The features of the toroidal solenoid, give it the simplicity to calculate the self-inductance.
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An ideal solenid of unknown length and cross-section has an inductance of 4.0mH. When current flows through the solenoid, there is an induced emf of 2.0V in the solenoid. Calculate the rate at which the current flowing through the solenoid is changing.
To explain self-inductance, it is helpful to consider the specific example of a long solenoid, as shown in the figure. This solenoid has only one winding, and so the EMF induced by its changing current appears across the solenoid itself. This contrasts with mutual inductance, where this voltage appears across a second coil wound on the same cylinder as the first.
Assume that the solenoid has radius R, length Z along the z axis, and is wound with nnn turns per unit length so that the total number of turns is equal to nZ. Assume that the solenoid is much longer than its radius.
A.
Suppose that the current varies with time, so that dI(t)/dt≠0. Find the electromotive force EMF induced across the entire solenoid due to the change in current through the entire solenoid.
Express your answer in terms of dI(t)/dt, n, Z, and R.
B.
The self-inductance L is related to the self-induced EMF E(t)by the equation E(t)=−LdI(t)/dtt. Find L for a long solenoid. (Hint: The self-inductance L will…
A long, current-carrying solenoid with an air core has 1700 turns per meter of length and a radius of 0.0195 m. A coil of 150 turns is wrapped tightly around the outside of the solenoid, so it has virtually the same radius as the solenoid. What is the mutual inductance of this system? Number Units
Chapter 30 Solutions
University Physics (14th Edition)
Ch. 30 - In an electric trolley or bus system, the vehicles...Ch. 30 - From Eq. (30.5) 1 H = 1 Wb/A. and from Eqs. (30.4)...Ch. 30 - Prob. Q30.3DQCh. 30 - Prob. Q30.4DQCh. 30 - Prob. Q30.5DQCh. 30 - Two closely wound circular coils have the same...Ch. 30 - Prob. Q30.7DQCh. 30 - For the same magnetic field strength B, is the...Ch. 30 - Prob. Q30.9DQCh. 30 - A Differentiating Circuit. The current in a...
Ch. 30 - In Section 30.5 Kirchhoffs loop rule is applied to...Ch. 30 - Prob. Q30.12DQCh. 30 - Prob. Q30.13DQCh. 30 - In the R-L circuit shown in Fig. 30.11, is the...Ch. 30 - Prob. Q30.15DQCh. 30 - In an L-R-C series circuit, what criteria could be...Ch. 30 - Prob. 30.1ECh. 30 - Prob. 30.2ECh. 30 - Prob. 30.3ECh. 30 - Prob. 30.4ECh. 30 - Prob. 30.5ECh. 30 - Prob. 30.6ECh. 30 - A 2.50-mH toroidal solenoid has an average radius...Ch. 30 - Prob. 30.8ECh. 30 - Prob. 30.9ECh. 30 - Prob. 30.10ECh. 30 - Prob. 30.11ECh. 30 - Prob. 30.12ECh. 30 - Prob. 30.13ECh. 30 - A long, straight solenoid has 800 turns. When the...Ch. 30 - Prob. 30.15ECh. 30 - Prob. 30.16ECh. 30 - Prob. 30.17ECh. 30 - Prob. 30.18ECh. 30 - Prob. 30.19ECh. 30 - Prob. 30.20ECh. 30 - In a proton accelerator used in elementary...Ch. 30 - It is proposed to store l.00 kWh = 3.60 106J of...Ch. 30 - Prob. 30.23ECh. 30 - Prob. 30.24ECh. 30 - Prob. 30.25ECh. 30 - In Fig. 30.11, switch S1 is closcd while switch S2...Ch. 30 - In Fig. 30.11, suppose that = 60.0 V, R = 240 ,...Ch. 30 - Prob. 30.28ECh. 30 - Prob. 30.29ECh. 30 - Prob. 30.30ECh. 30 - In an L-C circuit. L = 85.0 mH and C = 3.20F....Ch. 30 - Prob. 30.32ECh. 30 - A 7.50-nF capacitor is charged up to 12.0 V, then...Ch. 30 - Prob. 30.34ECh. 30 - Prob. 30.35ECh. 30 - A Radio Tuning Circuit. The minimum capacitance of...Ch. 30 - An L-C circuit containing an 80.0-mH inductor and...Ch. 30 - An L-R-C series circuit has L = 0.600 H and C =...Ch. 30 - Prob. 30.39ECh. 30 - An L-R-C series circuit has L = 0.400 H, C = 7.00...Ch. 30 - Prob. 30.41ECh. 30 - Prob. 30.42PCh. 30 - Prob. 30.43PCh. 30 - Prob. 30.44PCh. 30 - Solar Magnetic Energy. Magnetic fields within a...Ch. 30 - CP CALC A Coaxial Cable. A small solid conductor...Ch. 30 - Prob. 30.47PCh. 30 - CALC Consider the circuit in Fig. 30.11 with both...Ch. 30 - Prob. 30.49PCh. 30 - Prob. 30.50PCh. 30 - Prob. 30.51PCh. 30 - Prob. 30.52PCh. 30 - Prob. 30.53PCh. 30 - A 6.40-nF capacitor is charged to 24.0 V and then...Ch. 30 - An L-C circuit consists of a 60.0-mH inductor and...Ch. 30 - A charged capacitor with C = 590 F is connected in...Ch. 30 - CP In the circuit shown in Fig. P30.57, the switch...Ch. 30 - Prob. 30.58PCh. 30 - Prob. 30.59PCh. 30 - Prob. 30.60PCh. 30 - Prob. 30.61PCh. 30 - Prob. 30.62PCh. 30 - Prob. 30.63PCh. 30 - After the current in the circuit of Fig. P30.63...Ch. 30 - CP In the circuit shown in Fig. P30.65, switch S...Ch. 30 - Prob. 30.66PCh. 30 - Prob. 30.67PCh. 30 - Prob. 30.68PCh. 30 - Prob. 30.69PCh. 30 - CP A Volume Gauge. A tank containing a liquid has...Ch. 30 - Prob. 30.71CPCh. 30 - BIO QUENCHING AN MRI MAGNET. Magnets carrying very...Ch. 30 - BIO QUENCHING AN MRI MAGNET. Magnets carrying very...Ch. 30 - BIO QUENCHING AN MRI MAGNET. Magnets carrying very...Ch. 30 - BIO QUENCHING AN MRI MAGNET. Magnets carrying very...
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- Would the self-inductance of a 1.0 m long, tightly wound solenoid differ from the self-inductance per meter of in infinite, but otherwise identical, solenoid?arrow_forwardThe self-inductance of a coil is zero if there is no current passing through the windings. True or false?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
- A solenoid of N1turns has length l1and radius R1, and a second smaller solenoid of N2turns has length l2and radius R2. The smaller solenoid is placed completely inside the larger solenoid so that their long axes coincide. What is the mutual inductance of the two solenoids?arrow_forwardSuppose 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_forwardFor the circuit shown below, find the current through the inductor 2.0105 s after the switch is reopened.arrow_forward
- A coil of 40 turns is wrapped around a long solenoid of cross-sectional area 7.5 × 10-3 m2. The solenoid is 0.50 m long and has 500 turns. (a) What is the mutual inductance of this system? (b) The outer coil is replaced by a coil of 40 turns whose radius is three times that of the solenoid. What is the mutual inductance of this configuration?arrow_forwardShow that the expression for the magnetic field of a toroid reduces to tlrat for the field of an infinite solenoid in the limit that the cenmal radius goes to infinity.arrow_forward(a) Using the exact exponential treatment, find the time required for the current through a 2.00 H inductor in series with a 0.500 (resistor to be reduced to 0.100% of its original value. (b) Compare your answer to the approximate treatment using integral numbers of . (c) Discuss how signi?cant the difference is.arrow_forward
- Suppose that a rectangular toroid has 2000 windings and a self-inductance of 0.040 H. If h = 0.10 m, what is the current flowing through a rectangular toroid when the energy in its magnetic field is 2.0 × 10-6 J?arrow_forwardConsider an ideal solenoid X that carries a current 2I. Another solenoid is wrapped around solenoid X resulting to a mutual inductance of 2M . If the current in X is halved, what is the resulting mutual inductance?arrow_forwardA solenoid used in magnetic resonance imaging ("MRI") has to be large enough for a human being to fit inside the solenoid cylinder, where there is a strong, uniform magnetic field produced. One such solenoid is wound from lots of adjacent turns of a single layer of (niobium-titanium) superconducting wire 2mm in diameter. Using the approximate size of a human, estimate relevant parameters about the solenoid, and use them to estimate the self-inductance of this solenoid.arrow_forward
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