Pies

Almost everyone who works with electronic equipment has at some time verified that a capacitor can store energy. If the plates of a charged capacitor are connected by a con- ductor, such as a wire,charge moves between each plate and its connecting wire until the capacitor is uncharged. The discharge can often be observed as a visible spark. If you should accidentally touch the opposite plates ofa charged capacitor, your fingers act as a pathway for discharge, and the result is an electric shock. The degree of shock you receive depends on the capacitance and on the voltage applied to thecapacitor. Such a shock could be fatal if high voltages are present, such as in the power supply of a television set. Because the charges can be stored in a capacitor even when the set is turned off,unplugging the television does not make it safe to open the case and touch the components inside.
To calculate the energy stored in the capacitor, we shall assume a charging process that is differentfrom the actual process described in Section 26.1 but which gives the same final result. We can make this assumption because the energy in the final configu- ration does not depend on the actualcharge-transfer process. We imagine that the charge is transferred mechanically through the space between the plates. We reach in and grab a small amount of positive charge on the plate connected to thenegative terminal and apply a force that causes this positive charge to move over to the plate connected to the positive terminal. Thus, we do work on the charge as we transfer it from one plate to theother. At first, no work is required to transfer a small amount of charge dq from one plate to the other.3 However, once this charge has been trans- ferred, a small potential difference exists betweenthe plates. Therefore, work must be done to move additional charge through this potential difference. As more and more charge is transferred from one plate to the other, the potential difference...