Question

Two parallel plates, each of area A = 1m^2 are separated by a distance g. The electric field intensity between the plates is 3∗10^6 v/m. What is the force between the two plates?

(a) 1/2π∗10^3 N

(b) 1/8π∗10^3 N

(c) 8π∗10^3 N

(d) 0 N

This question was posed to me by my college professor while I was bunking the class.

The origin of the question is Singly Excited Electric Field Systems in division Basic Concepts in Rotating Machines of Electrical Machines

Answer 1

The correct choice is (b) 1/8π∗10^3 N

The best I can explain: When electric field is applied, the plates move towards each other because of force of attraction by a distance x ⇒ C = ε0A/(g-x)

Wfld(q,x) = 1/2 q^2/C = 1/2 q^2(g-x)/Aε0

fe = -∂Wfld(q,x)/∂x = 1/2q^2x/Aε0

We know, q = DA = ε0EA and ε0 = 10^-9/36Π

fe = 1/2 E^2ε0A = 1/2∗(3∗10^6)^2∗10^-9/36Π∗1 = 1/8π∗10^3 N