# The electric filed in a region is given by $\vec{E}=\left ( Ax+B \right )\hat{i}$, where E is in $NC^{-1}$ and x is in meters. The value of constantd are A=20 SI unit and B= 10 SI unit. If the potential at x=1 is V1 and that at x=-1 is V2 , then V1-V2 is: Option 1) 320 V Option 2) -48 V Option 3) 180 V Option 4) -520 V

Relation between E and V in integral form -

$\dpi{100} dV=-\int_{r_{1}}^{r_{2}}\overrightarrow{E}\cdot \vec{d}r=-\int_{r_{1}}^{r_{2}}Edr\cos \theta$

-

$V_{f}-V_{i}=-\int E.dx$

$V_{1}-V_{2}=\int_{-5}^{1}\left ( ax +b \right )dx$

$=-\left ( \frac{ax^{2}}{2} +bx\right )_{-5}^{1}$

$=-\left [\left ( \frac{a}{2} +b\right )-\left ( \frac{25a}{2} -5b\right ) \right ]$

$=-\left [\left ( \frac{20}{2} +10\right )-250+50 \right ]$

$=180V$

Option 1)

320 V

Option 2)

-48 V

Option 3)

180 V

Option 4)

-520 V

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