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Unit 2 Day 3: Electric Energy Storage • Electric potential energy stored between capacitor plates • Work done to add charge to the capacitor plates • Energy density of the electric field between capacitor plates • Movable parallel plate capacitor: change in electric potential energy vs. work done to move plates Energy Stored in a Capacitor • A charged capacitor stores electric potential energy in the electric field between the plates • The potential energy stored in the plates is equivalent to the work done to charge the plates. This work is usually done by a battery • As charge is added to the plates, it takes increasingly more work to add additional charge because of electron repulsion Energy Stored in a Capacitor dU V dq or dW V dq Q Q 2 1 q Q W V dq q dq 12 | 12 C0 C 0 C We can then say that the energy “stored” in the capacitor is: Since Q C V 2 C V U1 2 C 2 2 Q U 12 C W (J) 12 C V 2 A and V E d d Q (C) A then U 12 0 E 2 d 2 12 0 AdE 2 and u 12 0 E 2 is the energy density d Given C 0 Movable Parallel Plate Capacitor +Q -Q A The electric potential energy decreases as the plates are pulled apart x U + ΔV 0 AV 2 3x • The separation distance x, is increased to 3x, while the battery remains connected Movable Parallel Plate Capacitor • If the capacitor plate distance is increased with the battery remaining connected: – – – – – – • ΔV is constant A C Capacitance decreases d Charge decreases Q C V E decreases E lV Ue stored, decreases U A d E Energy density decreases u E 0 e 1 2 2 0 1 2 2 0 If the capacitor plate distance is increased with the battery removed: – – – – – – Charge is constant A Capacitance decreases C d Q V ΔV increases C Q E is unchanged E A Ue stored, increases U A d E Energy density is unchanged u 0 0 e 1 2 2 0 1 2 0E2