Question

A student makes a short electromagnet by winding 300 turns of wire around a wooden cylinder of diameter $d=5.0 \mathrm{~cm} .$ The coil is connected to a battery producing a current of $4.0 \mathrm{~A}$ in the wire. (a) What is the magnitude of the magnetic dipole moment of this device? (b) At what axial distance $z>d$ will the magnetic field have the magnitude $5.0 \mu \mathrm{T}$ (approximately one-tenth that of Earth's magnetic field)?

Name: Problem 57, Chapter 29: Fundamentals of Physics
Uploaded: 2021-09-06T15:00:03-08:00
Duration: 4 min 18 s
Channel: Vishal Gupta

   A student makes a short electromagnet by winding 300 turns of wire around a wooden cylinder of diameter $d=5.0 \mathrm{~cm} .$ The coil is connected to a battery producing a current of $4.0 \mathrm{~A}$ in the wire. (a) What is the magnitude of the magnetic dipole moment of this device? (b) At what axial distance $z>d$ will the magnetic field have the magnitude $5.0 \mu \mathrm{T}$ (approximately one-tenth that of Earth's magnetic field)?

Fundamentals of Physics

David Halliday,… 11th Edition

Chapter 29, Problem 57

Instant Answer

Solved by Expert Vishal Gupta

09/06/2021

Step 1

The magnetic dipole moment (m) is given by the formula m = NIA, where N is the number of turns, I is the current, and A is the area of the cross section of the coil. Given that N = 300 turns, I = 4.0 A, and the radius r = d/2 = 2.5 cm = 2.5 x 10^-2 m, we can Show more…

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A student makes a short electromagnet by winding 300 turns of wire around a wooden cylinder of diameter $d=5.0 \mathrm{~cm} .$ The coil is connected to a battery producing a current of $4.0 \mathrm{~A}$ in the wire. (a) What is the magnitude of the magnetic dipole moment of this device? (b) At what axial distance $z>d$ will the magnetic field have the magnitude $5.0 \mu \mathrm{T}$ (approximately one-tenth that of Earth's magnetic field)?

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Key Concepts

Magnetic Dipole Moment

This is a measure of the strength and orientation of a magnetic source, such as a current-carrying loop or coil. It is given by the product of the number of turns (N), the current (I), and the area (A) of the loop, expressed as m = NIA. The magnetic dipole moment characterizes how a magnetic object interacts with external magnetic fields by aligning with them, similar to how an electric dipole behaves in an electric field.

Magnetic Field of a Dipole

For points located along the axis of a magnetic dipole, the magnetic field decreases with distance in a specific manner, typically proportional to 1/z^3, where z is the axial distance from the dipole. The field can be approximated by the formula B = (?0/4?)(2m/z^3) for a small dipole, where ?0 is the permeability of free space and m is the magnetic dipole moment. This concept is crucial for understanding how the magnetic field strength diminishes as one moves away from the source.

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