A parallel-plate capacitor consists of two large, flat, horizontal metal plates separated by a distance d d\,d in a vacuum. The upper plate (at x=0x = 0x=0) is maintained at a steady potential +V0+V_0+V0, and the lower plate (at x=dx = dx=d) is connected to earth (0 V), as shown in the diagram.
Describe the mathematical relationship of both the electric field strength E E\,E and the electric potential V V\,V with respect to the distance x x\,x from the upper plate (for 0≤x≤d0 \le x \le d0≤x≤d).
Your answer should:
- State expressions for E E\,E and V(x)V(x)V(x) in terms of V0V_0V0, ddd, and xxx.
- Describe the key geometric features of the corresponding graphs of E E\,E versus x x\,x and V V\,V versus xxx.