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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 ??

Thanks!

Note by Karan Shekhawat
3 years, 2 months ago

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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 $$- \vec{p}.\vec{E}$$.

- 3 years, 2 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 ??

- 3 years, 2 months ago