Question

The electric field in a region of space is $eX=-1000\times v/M$, where $x$is in meters.

a. Graph $Ex$versus $x$over the region $-1m...\times ...1m$.

b. What is the potential difference between $xi=-20cm$and $xf=30cm$?

Short answer

a. The graph is given below.

b. The potential difference is$25V$.

Step-by-step solution

Part(a) step 1: Given information

We have given that the electric field in a region of space is $Ex=-1000xV/m$, where $x$is in meters.

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

Part (a) step 2: Simplify

The graph for the electric field is

Part (b) step 1: Given information

We have given that the the electric field in a region of space is $Ex=-1000xV/m$, where $x$is in meters.

We need to find the p.

Part (b) step 2: Simlplify 

The potential is given as

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

The potential difference is given as

$∆V={\int }_{-0.2}^{0.3}-1000xdx=500{\left[x^2\right]}_{-0.2}^{0.3}=500·(0.09-0.04)=25V$.