Ch 30: Electromagnetic Induction

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 30: Electromagnetic Induction

Problem 1

Chapter 30, Problem 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 $\vec{B}$ .

Verified step by step guidance

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 = B l v

, 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 = \frac{ε}{B l}

Step 3: Substitute the given values into the formula. The emf

ε

is 1.0 V, the magnetic field strength

B

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 = \frac{1.0}{5.0×10−5 \times 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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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.

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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Textbook Question

What is the magnitude of the magnetic flux through the loop shown in FIGURE EX30.5?

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Textbook Question

A potential difference of 0.050 V is developed across the 10-cm-long wire of FIGURE EX30.3 as it moves through a magnetic field perpendicular to the figure. What are the strength and direction (in or out) of the magnetic field?

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Textbook Question

INT A 10-cm-long wire is pulled along a U-shaped conducting rail in a perpendicular magnetic field. The total resistance of the wire and rail is 0.20 Ω. Pulling the wire at a steady speed of 4.0 m/s causes 4.0 W of power to be dissipated in the circuit. How big is the pulling force?

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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→\(\overrightarrow{B}\).

Verified video answer for a similar problem:

Key Concepts

Motional Electromotive Force (emf)

Magnetic Field Strength

Perpendicular Motion

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 $\vec{B}$ .