In this quick derivation of energy density in the electric field, we shift our perspective on the energy stored in a parallel plate capacitor. Instead of thinking about the work it takes to move charge from one plate to the other, we shift to thinking about it as the energy stored in the electric field itself!
We originally computed the energy stored in a capacitor by calculating the work required to move charge from one plate to the other, and that derivation can be found here: • Energy of a capacitor ...
Now we shift to thinking about the energy stored in a capacitor as the energy density in the electric field in the region between the plates of the parallel plate capacitor. We take the total energy in the capacitor U=1/2*C*V^2 and divide by the volume between the plates of the capacitor, which is given by the area of the plates multiplied by the plate separation distance A*d.
Next, we use the formula for the capacitance given area and distance between the plates, which was derived here: • Introduction to capaci... so we can replace C with epsilon_0*A/d.
After simplifying, we find that the energy density in the electric field is given by u=1/2*epsilon_0*E^2, where E is the electric field between the plates.
This result is true in general of any region with electric field in it, and now we can calculate the energy stored in a charge configuration by integrating the energy density over the space around the distribution!
Two applications of the electric field energy density formula will be linked in the endscreen when they are finished: the energy stored in a concentric cylindrical shell capacitor and the energy stored in a nested spherical shell capacitor.
Негізгі бет Quick derivation of energy density in the electric field using a parallel plate capacitor.
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