Magnetic Energy in 2-D object?

How can I calculate magnetic energy ( OR You can say Electrostatic energy which is more correct to say) stored in an 2-D object ?

I mean to say That If I know B=F(x) in an 2-D figure say Circle Then how Can I calculate magnetic energy in that area??

I know that Magnetic energy stored per unit volume is $\frac { { B }^{ 2 } }{ 2{ \mu }_{ 0 } }$ .

But can I use same result for magnetic energy per unit area ??

Please help me I'm too confused!

Thanks!

#ElectricityAndMagnetism #Energy #HelpMe!

Easy Math Editor

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

Markdown	Appears as
`italics` or `_italics_`	italics
`bold` or `__bold__`	bold
- bulleted - list	bulleted list
1. numbered 2. list	numbered list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1 paragraph 2	paragraph 1 paragraph 2
`[example link](https://brilliant.org)`	example link
`> This is a quote`	This is a quote
# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"	# I indented these lines # 4 spaces, and now they show # up as a code block. print "hello world"

Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

@Ronak Agarwal @Mvs Saketh @jatin yadav or any other please Help

Karan Shekhawat - 6 years, 7 months ago

The value of energy stored due to magnetic field in a given finite area is $0$ . But if this is an area enclosed by a wire carrying current, the magnetic energy is $-\vec{M}\cdot \vec{B}$ . Compare this to an electric dipole in electric field. The energy $\dfrac{1}{2} \epsilon_{0} E^2 dV$ is different from $- \vec{p}.\vec{E}$ .

jatin yadav - 6 years, 7 months ago

ohh.... Thanks a lot!

But I have doubt that if that magnetic field vary with Time then still Magnetic (or actually Electrostatic ) energy stored is zero ??

Karan Shekhawat - 6 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$