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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Ch 30: Inductance
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
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- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 30, Problem 1a
Two coils have mutual inductance M = 3.25 × 10-4 H. The current i1 in the first coil increases at a uniform rate of 830 A/s. What is the magnitude of the induced emf in the second coil? Is it constant?
Verified step by step guidance1
Understand the concept of mutual inductance: Mutual inductance is the property of two coils where a change in current in one coil induces an electromotive force (emf) in the other coil. The mutual inductance M is a measure of how effectively a change in current in one coil induces an emf in the other.
Recall the formula for induced emf due to mutual inductance: The induced emf (ε) in the second coil can be calculated using the formula: , where M is the mutual inductance and is the rate of change of current in the first coil.
Substitute the given values into the formula: You are given M = 3.25 × 10-4 H and = 830 A/s. Substitute these values into the formula to find the induced emf.
Calculate the magnitude of the induced emf: Perform the multiplication to find the magnitude of the induced emf in the second coil. The result will give you the magnitude of the induced emf.
Determine if the induced emf is constant: Since the rate of change of current is constant, the induced emf will also be constant over time.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Mutual Inductance
Mutual inductance is a measure of the ability of one coil to induce an electromotive force (emf) in another coil when the current in the first coil changes. It is denoted by M and is measured in henries (H). The mutual inductance depends on factors like the number of turns in the coils, their orientation, and the medium between them.
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Mutual Induction
Faraday's Law of Electromagnetic Induction
Faraday's Law states that a change in magnetic flux through a circuit induces an electromotive force (emf) in the circuit. The induced emf is proportional to the rate of change of the magnetic flux. In the context of mutual inductance, the induced emf in the second coil is given by the product of the mutual inductance and the rate of change of current in the first coil.
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Rate of Change of Current
The rate of change of current refers to how quickly the current in a circuit is increasing or decreasing over time. It is expressed in amperes per second (A/s). In this problem, the current in the first coil changes at a uniform rate, which means the induced emf in the second coil will be constant, as it depends linearly on this rate of change.
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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. 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
A 2.50-mH toroidal solenoid has an average radius of 6.00 cm and a cross-sectional area of 2.00 cm2. How many coils does it have? (Make the same assumption as in Example 30.3.)
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