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Ch 30: Electromagnetic Induction
Knight Calc - Physics for Scientists and Engineers 5th Edition
Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoKnight Calc 5th EditionCh 30: Electromagnetic InductionProblema 1
Capitolo 30, Problema 1

The earth’s magnetic field strength is 5.0×10−5 T. How fast would you have to drive your car to create a 1.0 V motional emf along your 1.0-m-tall radio antenna? Assume that the motion of the antenna is perpendicular to B→\(\overrightarrow{B}\).

Guida verificata passo dopo passo
1
Step 1: Understand the concept of motional emf. Motional emf is generated when a conductor moves through a magnetic field, and it is given by the formula: ε=Blv, where ε is the emf, B is the magnetic field strength, l is the length of the conductor, and v is the velocity of the conductor.
Step 2: Rearrange the formula to solve for velocity v. The formula becomes: v=εBl.
Step 3: Substitute the given values into the formula. The emf ε is 1.0 V, the magnetic field strength B is 5.0×10−5 T, and the length of the antenna l is 1.0 m.
Step 4: Perform the substitution into the formula: v=1.05.0×10−5×1.0. This will give the velocity required to generate the specified emf.
Step 5: Interpret the result. The calculated velocity will represent how fast the car must move perpendicular to the magnetic field to produce a motional emf of 1.0 V along the 1.0-m-tall antenna.

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Motional Electromotive Force (emf)

Motional emf is generated when a conductor moves through a magnetic field, inducing a voltage across the conductor. The magnitude of the induced emf can be calculated using the formula emf = B * L * v, where B is the magnetic field strength, L is the length of the conductor, and v is the velocity of the conductor relative to the magnetic field.
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Motional EMF

Magnetic Field Strength

Magnetic field strength, measured in teslas (T), quantifies the intensity of a magnetic field. In this context, the Earth's magnetic field strength is given as 5.0×10^−5 T, which influences the amount of emf generated when a conductor moves through it. Understanding this value is crucial for calculating the required speed to achieve a specific emf.
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Magnetic Fields and Magnetic Dipoles

Perpendicular Motion

When the motion of a conductor is perpendicular to the magnetic field lines, the induced emf is maximized. This is because the angle between the velocity vector of the conductor and the magnetic field vector is 90 degrees, leading to the most effective interaction. In this problem, the assumption that the antenna moves perpendicularly to the magnetic field is essential for applying the motional emf formula correctly.
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Find Field due to Two Perpendicular Currents
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