91Ó°ÊÓ

We have given that the electric field in a region of space is$E_x=5000xV/m$, where $x$is in meters.

We need to find the graph $Ex$versus $x$over the region $-1m...×...1m$.

The graph of the electric field with respect to the position, is given in the figure, to the left

We have given that the electric field in a region of space is $E_x=5000xV/m$where $x$is in meters.

We need to find that an expression for the potential $V$at position $x$. As a reference, let $V=0V$at the origin.

The electric field $E$is given. So, the potential is given as

$V\left(x\right)=-E\left(x\right)dx$

For the potential at a specific position, we can integrate from zero to the given position, and we have to add no constant in the integration as we are given $V\left(o\right)=0$. That is,

$V\left(x\right)={∫}_0^{x}E\left(x\right)dx=-2500x^2$

We have given that the electric field in a region of space is$E_x=5000xV/m$where $x$is in meters.

We need to find graph $V$versus $x$over the region $-1m...×...1m$.

The graph of$V$versus$x$is given as