A parallel plate capacitor is formed by two large, flat, conducting plates, which – [Free] B50
A parallel plate capacitor is formed by two large, flat, conducting plates, which are parallel to each other. The left plate has a surface charge density of + π +Ο The right plate has a surface charge density of β π βΟ Find the electric field vectors (magnitude and direction) at the following regions:
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𧲠Electric Field Due to Two Parallel Plates
Two infinite parallel plates are given:
- The left plate has a surface charge density of +Ο.
- The right plate has a surface charge density of βΟ.
π Basic Formula: Electric Field from a Charged Plate
The electric field due to a single infinite sheet of charge is given by:
Direction:
- Positive charge (+Ο) β field points away from the plate.
- Negative charge (βΟ) β field points toward the plate.
π Region-wise Electric Field Calculation
a) Left of the Plates
Field from left plate: leftward β \( \frac{Ο}{2Ξ΅β} \)
Field from right plate: rightward β \( \frac{Ο}{2Ξ΅β} \)
Fields cancel out: Eleft = 0 N/C
b) Between the Plates
Field from left plate: rightward β \( \frac{Ο}{2Ξ΅β} \)
Field from right plate: rightward β \( \frac{Ο}{2Ξ΅β} \)
Fields add up: Ebetween = Ο / Ξ΅β
c) Right of the Plates
Field from left plate: rightward β \( \frac{Ο}{2Ξ΅β} \)
Field from right plate: leftward β \( \frac{Ο}{2Ξ΅β} \)
Fields cancel out: Eright = 0 N/C
π Final Summary Table
| Region | Electric Field Magnitude | Direction |
|---|---|---|
| Left of the Plates | 0 N/C | β |
| Between the Plates | Ο / Ξ΅β | To the right |
| Right of the Plates | 0 N/C | β |