Ch 29: The Magnetic Field

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 29: The Magnetic Field

Problem 52b

Chapter 29, Problem 52b

The heart produces a weak magnetic field that can be used to diagnose certain heart problems. It is a dipole field produced by a current loop in the outer layers of the heart. What is the magnitude of the heart's magnetic dipole moment?

Verified step by step guidance

Understand the concept of a magnetic dipole moment: The magnetic dipole moment (\( \mu \)) is a measure of the strength of a magnetic source and is given by the formula \( \mu = I \cdot A \), where \( I \) is the current and \( A \) is the area of the current loop.

Identify the parameters: Determine the current \( I \) flowing through the loop and the area \( A \) of the loop. The area \( A \) can be calculated using \( A = \pi r^2 \), where \( r \) is the radius of the loop.

Substitute the values into the area formula: Use the given or estimated radius of the current loop to calculate \( A \) using \( A = \pi r^2 \). Ensure the radius is in meters for SI unit consistency.

Calculate the magnetic dipole moment: Substitute the values of \( I \) (current) and \( A \) (area) into the formula \( \mu = I \cdot A \). This will give the magnitude of the magnetic dipole moment in units of \( \text{A} \cdot \text{m}^2 \) (ampere-square meters).

Verify the units and interpret the result: Ensure that the units of the calculated magnetic dipole moment are consistent with \( \text{A} \cdot \text{m}^2 \). This value represents the strength of the heart's magnetic field and can be used for diagnostic purposes.

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Key Concepts

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

Magnetic Dipole Moment

The magnetic dipole moment is a vector quantity that represents the strength and orientation of a magnetic source. In the context of the heart, it arises from the electrical currents generated by the heart's muscle contractions. The dipole moment is crucial for understanding how the heart's magnetic field interacts with external magnetic fields and can be measured to assess heart health.

Current Loop

A current loop is a closed loop through which electric current flows, generating a magnetic field. In the heart, the arrangement of muscle fibers and the flow of ionic currents during heartbeats create such loops. The characteristics of these loops, including their size and current strength, directly influence the resulting magnetic dipole moment of the heart.

Magnetic Field Measurement

Magnetic field measurement involves quantifying the strength and direction of magnetic fields, often using instruments like magnetometers. For the heart, techniques such as magnetocardiography can detect the weak magnetic fields produced by the heart's electrical activity. Understanding how to measure these fields is essential for diagnosing heart conditions and evaluating the heart's magnetic dipole moment.

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