Question

What is the electric field inside a capacitor?

Answer 1

1. Capacitor is a device that is used to store electrical energy. The most common type of a capacitor is the parallel plate capacitor.
2. It consists of two conducting plates placed close and parallel to each other.
3. The electric field due to an infinitely large charged plate is, $E=\frac{\sigma }{2{\epsilon }_0}$. Here, $\sigma$ is the surface charge density and ${\epsilon }_0$ is the permittivity of free space.
4. Since the plates of a capacitor are very close to each other, they can be considered to be infinitely large. This is because the distance from the plate, where the electric field is measured, is negligible compared to the surface area of the plate.
5. The two plates of a charged capacitor have equal and opposite charge. Hence, the magnitude of the surface charge density of both the plates will be the same.
6. Since, the electric field due to both the charged plates are in the same direction, the net electric field inside the capacitor will add up.

$\begin{array}{rcl}{E}_{net}& =& E_{+}+E_{-}\\ & =& \frac{\sigma }{2{\epsilon }_0}+\frac{\sigma }{2{\epsilon }_0}\\ & =& \frac{\sigma }{{\epsilon }_0}\end{array}$

Here, $E_{+}$ is the field due to the positive plate and $E_{-}$ is the field due tot he negative plate. Hence, the electric field inside the capacitor is $E=\frac{\sigma }{{\epsilon }_0}$.