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 40

Chapter 29, Problem 40

A small bar magnet experiences a 0.020 N m torque when the axis of the magnet is at 45° to a 0.10 T magnetic field. What is the magnitude of its magnetic dipole moment?

Verified step by step guidance

Understand the relationship between torque, magnetic dipole moment, magnetic field, and the angle between them. The formula is:

τ = m B sin θ

, where

τ

is the torque,

m

is the magnetic dipole moment,

B

is the magnetic field strength, and

θ

is the angle between the magnetic field and the dipole axis.

Rearrange the formula to solve for the magnetic dipole moment

m

m = \frac{τ}{B}

Substitute the given values into the formula:

τ = 0.020

N·m,

B = 0.10

T, and

θ = 45°

. Note that

sin(45°) = \sqrt{\frac{1}{2}}

Simplify the denominator by calculating

B sin θ

B sin(45°) = 0.10 × \sqrt{\frac{1}{2}}

Divide the torque by the result from the previous step to find the magnetic dipole moment

m

m = \frac{0.020}{0.10 \times \sqrt{\frac{1}{2}}}

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Key Concepts

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

Torque on a Magnetic Dipole

Torque ( au) on a magnetic dipole in a magnetic field is given by the equation τ = μB sin(θ), where μ is the magnetic dipole moment, B is the magnetic field strength, and θ is the angle between the dipole moment and the magnetic field. This relationship shows how the orientation of the dipole affects the torque it experiences in the field.

Magnetic Dipole Moment

The magnetic dipole moment (μ) is a vector quantity that represents the strength and orientation of a magnet. It is defined as the product of the current flowing through a loop and the area of the loop, or for a bar magnet, it can be thought of as a measure of how much torque it will experience in a magnetic field. The unit of magnetic dipole moment is Am².

Magnetic Field Strength

Magnetic field strength (B) is a measure of the magnetic force experienced by a unit magnetic pole in a magnetic field. It is expressed in teslas (T) and indicates the intensity of the magnetic field. In the context of the question, a magnetic field strength of 0.10 T is applied, influencing the torque experienced by the bar magnet.

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