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Explain why the work needed to move a particle with charge Q through a potential differenceΔV is W = QΔV, whereas the energy stored in a charged capacitor is U =1/2QΔV. Where does the ½ factor come from?

Explain why the work needed to move a particle with charge Q through a potential differenceΔV is W = QΔV, whereas the energy stored in a charged capacitor is U =1/2QΔV. Where does  the ½ factor come from?

Grade:Upto college level

1 Answers

SAGAR SINGH - IIT DELHI
879 Points
10 years ago

Dear sunil,

Work must be done by an external influence to "move" charge between the conductors in a capacitor. When the external influence is removed the charge separation persists in the electric field and energy is stored to be released when the charge is allowed to return to its equilibrium position. The work done in establishing the electric field, and hence the amount of energy stored, is given by:

 

W= \int_{q=0}^Q V \text{d}q = \int_{q=0}^Q \frac{q}{C} \text{d}q = {1 \over 2} {Q^2 \over C} = {1 \over 2}  C V^2 = {1 \over 2} VQ.

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