Chapter 7.1, Problem 7R

To determine

To calculate:Number ofmagnetic domains in the magnet.

Answer to Problem 7R

Number ofmagnetic domains in the magnet is $\underset{\_}{20,000,000}$ .

Explanation of Solution

Given:

Volume of a magnetic domain = $\text{0}{\text{.0001 mm}}^3$

Length of magnet = $\text{50 mm}$

Width of magnet = $\text{10 mm}$

Height of magnet = $\text{4 mm}$

Formula used:

Volume is given by,

  $V=l\times w\times h$

where $l$ is length, $w$ is width and $h$ is height.

Calculation:

To calculate the number of domains in the magnet, first calculate the volume of the magnet.

Volume is calculated as:

  $\begin{array}{l}V=l\times w\times h\\ =(50\text{ mm})(10\text{ mm})(4\text{ mm})\\ =2000{\text{ mm}}^3\end{array}$

Number of magnetic domains is:

  $\begin{array}{l}\frac{\text{Volume of magnet}}{\text{Volume of each magnetic domain}}\\ =\frac{2000{\text{ mm}}^3}{0.0001{\text{ mm}}^3}\\ =20,000,000\end{array}$

Conclusion:

Number ofmagnetic domains in the magnet is $\underset{\_}{20,000,000}$ .