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| 1. |
Show that the force on each plate of a parallel plate capacitor has a magnitude equal to (1//2)QE, where Q is the charge on the capacitor, and E is the magnitude of electric field between the plates. Explain the origin of the factor 1//2. |
| Answer» Solution :Hint: Suppose we increase the separation of the plates by `Deltax` . Work done (by external agency) = F =`Deltax` . This goes to increase the potential ENERGY of the capacitor by u a`Deltax`where u is energy density. Therefore, F = u a which is easily seen to be (1/2) QE, USING `u = (1//2) epsilon_(0)E^(2)`. The physical origin of the factor 1/2 in the force formula lies in the fact that just OUTSIDE the conductor, field is E, and inside it is zero. So, the average value E/2 CONTRIBUTES to the force. | |