Question

The electric potential in a region of uniform electric field is$-1000V$ at $x=-1.0m$ and $+1000V\mathrm{at}x=+1.0m$. What is $E_x$?

Short answer

$E_x=\mathbf{-}\mathbf{1000}\mathbf{}\mathit{V}\mathbf{/}\mathit{m}$

Step-by-step solution

Given information and theory used   

Given :

The electric potential is : $-1000V\mathrm{at}x=-1.0m$ and

$+1000V\mathrm{at}x=+1.0m.$

Theory used :

The electric field is expressed as a function of potential as :

$E\left(x\right)=-\frac{dV\left(x\right)}{dx}$

Calculating Ex 

In a given region, the uniform electric field is equal to minus the difference in potential divided by distance.

So,

$E_x=-\frac{1000V-(-1000V)}{1m-(-1m)}=\boxed{\mathbf{-}\mathbf{1000}\mathbf{}\mathit{V}\mathbf{/}\mathit{m}}$ is the result.