Textbook Question
An air-filled toroidal solenoid has a mean radius of 15.0 cm and a cross-sectional area of 5.00 cm2. When the current is 12.0 A, the energy stored is 0.390 J. How many turns does the winding have?
Ch 30: Inductance
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors37
- Ch 02: Motion Along a Straight Line57
- Ch 03: Motion in Two or Three Dimensions45
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws54
- Ch 06: Work & Kinetic Energy11
- Ch 07: Potential Energy & Conservation6
- Ch 08: Momentum, Impulse, and Collisions15
- Ch 09: Rotation of Rigid Bodies37
- Ch 10: Dynamics of Rotational Motion44
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics27
- Ch 13: Gravitation34
- Ch 14: Periodic Motion26
- Ch 15: Mechanical Waves22
- Ch 16: Sound & Hearing28
- Ch 17: Temperature and Heat28
- Ch 18: Thermal Properties of Matter35
- Ch 19: The First Law of Thermodynamics29
- Ch 20: The Second Law of Thermodynamics18
- Ch 21: Electric Charge and Electric Field28
- Ch 22: Gauss' Law21
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF24
- Ch 26: Direct-Current Circuits29
- Ch 27: Magnetic Field and Magnetic Forces16
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction22
- Ch 30: Inductance14
- Ch 31: Alternating Current20
- Ch 33: The Nature and Propagation of Light17
- Ch 34: Geometric Optics29
- Ch 35: Interference13
- Ch 36: Diffraction19
- Ch 37: Special Relativity19
- Ch 38: Photons: Light Waves Behaving as Particles12
- Ch 39: Particles Behaving as Waves25
- Ch 40: Quantum Mechanics I: Wave Functions20
- Ch 41: Quantum Mechanics II: Atomic Structure21
- Ch 42: Molecules and Condensed Matter17
- Ch 43: Nuclear Physics13
- Ch 44: Particle Physics and Cosmology17
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 30, Problem 10a
The inductor shown in Fig. E30.11 has inductance 0.260 H and carries a current in the direction shown. The current is changing at a constant rate. The potential between points a and b is Vab = 1.04 V, with point a at higher potential. Is the current increasing or decreasing?
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Identify the given values: The inductance of the inductor is 0.260 H, and the potential difference between points a and b is Vab = 1.04 V, with point a at a higher potential.
Recall the formula for the potential difference across an inductor: V = L * (di/dt), where V is the potential difference, L is the inductance, and di/dt is the rate of change of current.
Since point a is at a higher potential than point b, the potential difference Vab is positive. This indicates that the induced emf opposes the change in current according to Lenz's Law.
Determine the direction of the current change: If the current were increasing, the induced emf would oppose the increase, making point b higher in potential than point a. Since point a is higher, the current must be decreasing.
Conclude that the current is decreasing because the positive potential difference indicates that the induced emf is acting to oppose a decrease in current.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Inductance
Inductance is a property of an electrical conductor, typically a coil, that quantifies its ability to oppose changes in current. It is measured in henries (H) and is determined by the coil's geometry and the number of turns. An inductor stores energy in a magnetic field when current flows through it, and this energy opposes changes in the current.
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Mutual Induction
Electromotive Force (EMF) in Inductors
The electromotive force (EMF) induced in an inductor is due to the change in current flowing through it. According to Faraday's Law, the EMF is proportional to the rate of change of current and the inductance. The direction of the induced EMF opposes the change in current, as described by Lenz's Law, which is why point a is at a higher potential when the current is decreasing.
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Potential Difference
Potential difference, or voltage, between two points in a circuit is the work needed to move a charge between those points. In the context of an inductor, the potential difference is influenced by the induced EMF due to changing current. If point a is at a higher potential than point b, it indicates that the EMF is opposing the current flow, suggesting the current is decreasing.
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Related Practice
Textbook Question
At the instant when the current in an inductor is increasing at a rate of 0.0640 A/s, the magnitude of the self-induced emf is 0.0160 V. What is the inductance of the inductor?
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Textbook Question
At the instant when the current in an inductor is increasing at a rate of 0.0640 A/s, the magnitude of the self-induced emf is 0.0160 V. If the inductor is a solenoid with 400 turns, what is the average magnetic flux through each turn when the current is 0.720 A?
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Textbook Question
When the current in a toroidal solenoid is changing at a rate of 0.0260 A/s, the magnitude of the induced emf is 12.6 mV. When the current equals 1.40 A, the average flux through each turn of the solenoid is 0.00285 Wb. How many turns does the solenoid have?
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Textbook Question
A long, straight solenoid has 800 turns. When the current in the solenoid is 2.90 A, the average flux through each turn of the solenoid is 3.25 × 10-3 Wb. What must be the magnitude of the rate of change of the current in order for the self-induced emf to equal 6.20 mV?
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Textbook Question
Inductance of a Solenoid. A metallic laboratory spring is typically 5.00 cm long and 0.150 cm in diameter and has 50 coils. If you connect such a spring in an electric circuit, how much self-inductance must you include for it if you model it as an ideal solenoid?
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