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notes24 2317

# notes24 2317 - ECE 2317 ECE Applied Electricity and...

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Prof. David R. Jackson ECE Dept. Spring 2011 Notes 24 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism

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Stored Energy Stored Energy 1 2 E v V U dV ρ = Φ 1 2 E V U D E dV = ( 29 0 Φ ∞ = Please see the textbook for a derivation of these formulas. 1 2 E s S U dS ρ = Φ Charge formula: Electric-field formula: (volume charge density) (surface charge density) These charge-density formulas require
Example Example + - ε r h x V 0 A [m 2 ] Method #1 0 0 0 2 0 0 1 2 ˆ ˆ 1 2 E V r E r V U D E dV V E x h V D x h V U dV h ε ε ε ε = = = = Find the stored energy (Use electric field formula)

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Example (cont.) Example (cont.) ( 29 [ ] 2 0 0 J 1 2 E r V U Ah h ε ε = 2 0 0 1 2 E r A U V h ε ε = or 2 0 1 2 E U CV = Recall that 0 r A C h ε ε = Hence
Example (cont.) Example (cont.) Method #2 1 2 1 1 2 2 A B E s S A s B s S S U dS dS dS ρ ρ ρ = Φ = Φ + Φ (since we have surface charge in this problem)

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notes24 2317 - ECE 2317 ECE Applied Electricity and...

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