# lecture12 - Physics for Scientists& Engineers 2 Chapter...

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Unformatted text preview: September 22, 2011 Physics for Scientists & Engineers 2, Chapter 24 1 September 22, 2011 Physics for Scientists & Engineers 2, Chapter 24 2 A battery must do work to charge a capacitor We can think of this work as changing the electric potential energy of the capacitor e differential work dW done by a battery with a potential difference Δ V’ to put a differential charge dq’ on a capacitor with capacitance C is e total work required to bring the capacitor to its full charge q is dW = Δ V ' dq ' = q ' C dq ' W t = dW ∫ = q ' C dq ' q ∫ = 1 2 q 2 C September 22, 2011 Physics for Scientists & Engineers 2, Chapter 24 3 is work is stored as electric potential energy We de ne the electric energy density , u , as the electric potential energy per unit volume Taking the case of an ideal parallel plate capacitor U = 1 2 q 2 C = 1 2 C Δ V ( ) 2 = 1 2 q Δ V ( ) u = U volume u = U Ad = 1 2 C Δ V ( ) 2 Ad = C Δ V ( ) 2 2 Ad September 22, 2011 Physics for Scientists & Engineers 2, Chapter 24 4 Inserting our formula for the capacitance of a parallel plate capacitor we nd Recognizing that Δ V / d is the magnitude of the electric eld, E , we obtain an expression for the electric energy density for parallel plate capacitor is result, which we derived for the parallel plate capacitor, holds for the electric potential energy stored in any electric eld per unit volume occupied by that eld u = ε A d ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ Δ V ( ) 2 2 Ad = 1 2 ε Δ V d ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 u = 1 2 ε E 2 September 22, 2011 Physics for Scientists & Engineers 2, Chapter 24 6 So far, we have discussed capacitors with air or vacuum between the plates However, most real-life capacitors have an insulating material, called a dielectric , between the two plates e dielectric serves several purposes: • Provides a convenient way to maintain mechanical separation between the plates • Provides electrical insulation between the plates • Allows the capacitor to hold a higher voltage • Increases the capacitance of the capacitor • Takes advantage of the molecular structure of the dielectric material Demo September 22, 2011 Physics for Scientists & Engineers 2, Chapter 24 7 Placing a dielectric between the plates of a capacitor increases the capacitance of the capacitor by a numerical factor called the dielectric constant , κ We can express the capacitance of a capacitor with a dielectric with dielectric constant κ between the plates as Where...
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lecture12 - Physics for Scientists& Engineers 2 Chapter...

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