Chapter 32: Q41P (page 969)

A magnet in the form of a cylindrical rod has a length of $5.00 cm$ and a diameter of $1.00 cm$ . It has a uniform magnetization of $5.30 \times 10^{3} A / m$ . What is its magnetic dipole moment?

Short Answer

Expert verified

The magnetic dipole moment is $2.08 \times 10^{- 2} J / T$ .

Step by step solution

Listing the given quantities

Length of cylinder, $l = 5.0 \times 10^{- 2} m$

Diameter of cylinder, $2 r = 1.0 \times 10^{- 2} m$

Magnetization, $M = 5.3 \times 10^{3} A / m$

Understanding the concepts of magnetization

We know that magnetic moment per unit volume is magnetization. We can find the magnetic dipole moment by substituting the given values in the formula for magnetization.

Formula:

$μ = M \cdot {πr}^{2} l$

Step 3: Calculations of the magnetic dipole moment

Magnetization is given by

$M = \frac{μ}{V}$

Where, $V$ is the volume and $μ$ is the magnetic dipole moment

The volume of the cylinder is given by $V = {πr}^{2} l$

Therefore,

$\begin{matrix} M = \frac{μ}{V} \\ = \frac{μ}{{πr}^{2} l} \end{matrix}$

Rearranging the above equation, we get,

$\begin{matrix} μ = M \cdot {πr}^{2} l \\ = (5.3 \times 10^{3}) \times π \times {(0.5)}^{2} \times 10^{- 4} \times 5.0 \times 10^{- 2} \\ = 2.08 \times 10^{- 2} J / T \end{matrix}$

The magnetic dipole moment is $2.08 \times 10^{- 2} J / T$ .

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A magnet in the form of a cylindrical rod has a length of $5.00 cm$ and a diameter of $1.00 cm$ . It has a uniform magnetization of $5.30 \times 10^{3} A / m$ . What is its magnetic dipole moment?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concepts of magnetization

Step 3: Calculations of the magnetic dipole moment

One App. One Place for Learning.

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A magnet in the form of a cylindrical rod has a length of 5.00cmand a diameter of1.00cm. It has a uniform magnetization of5.30×103A/m. What is its magnetic dipole moment?

Short Answer

Step by step solution

Listing the given quantities

Understanding the concepts of magnetization

Step 3: Calculations of the magnetic dipole moment

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Nuclear Physics

Further Mechanics and Thermal Physics

Radiation

Modern Physics

Fields in Physics

Translational Dynamics

Study anywhere. Anytime. Across all devices.

A magnet in the form of a cylindrical rod has a length of $5.00 cm$ and a diameter of $1.00 cm$ . It has a uniform magnetization of $5.30 \times 10^{3} A / m$ . What is its magnetic dipole moment?