EEE224_Fall09_magnetic_energy_force

EEE224_Fall09_magnetic_energy_force - METU - NCC EEE 224...

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1 EEE 224 ELECTROMAGNETIC THEORY Magnetic Energy and Forces METU - NCC
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2 Magnetic Energy Work must be done to send currents into conducting loops. This work is stored as “magnetic energy”. B H μ =
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3 Magnetic Energy Analogy between electrostatics and magnetostatics energies: Q C V = Electrostatics Magnetostatics 2 1 2 e WC V = 2 1 2 m WL I = 2 11 22 e VV WE D d v E d v ε =⋅ = ∫∫ 2 m WB H d v H d v μ =⋅= L I Λ =
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4 Example: Remember the coaxial cable question that we have solved previously Magnetic Energy a b Top view 0 2 0 ˆ 2 ˆ 2 0 Ir ai f ra a I f a r b B r if r b φ μ π = We have previously found B as follows by using Ampere’s law: Find the self-inductance of the cable by using magnetic energy.
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5 Example (continued. .): Magnetic Energy 2 ,0 1 28 m inner I W μ π = 2 , 0 2 12 0 2 0 000 2 0 11 1 22 1 in minner VV a zr WB H d v B d v Ir rdrd dz a I φ μπ === =⋅ = ⎛⎞ = ⎜⎟ ⎝⎠ = ∫∫ ∫∫∫ For r <a : Compare with 2 , 1 2 m inner inner WL I = 0 8 inner L = (H/m)
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EEE224_Fall09_magnetic_energy_force - METU - NCC EEE 224...

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