Answer
(a) $E_x = 500~V/m$
(b) $E_x = -1000~V/m$
(c) $E_x = 500~V/m$
Work Step by Step
(a) We can find $E_x$ at the point $x = -2~cm$:
$E_x = -\frac{\Delta V}{\Delta x}$
$E_x = -\frac{0-(-10~V)}{-0.03~m-(-0.01~m)}$
$E_x = -\frac{10~V}{-0.02~m}$
$E_x = 500~V/m$
(b) We can find $E_x$ at the point $x = 0~cm$:
$E_x = -\frac{\Delta V}{\Delta x}$
$E_x = -\frac{10~V-(-10~V)}{0.01~m-(-0.01~m)}$
$E_x = -\frac{20~V}{0.02~m}$
$E_x = -1000~V/m$
(c) We can find $E_x$ at the point $x = 2~cm$:
$E_x = -\frac{\Delta V}{\Delta x}$
$E_x = -\frac{0-(10~V)}{0.03~m-(0.01~m)}$
$E_x = -\frac{-10~V}{0.02~m}$
$E_x = 500~V/m$
