1. Tardigrade
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  3. Physics
  4. The electric field in a region is given by vecE = (Ax + B) hati where E is in NC-1and x is in metres. The values of constants are A = 20 SI unit and B = 10 SI unit. If the potential at x = 1 is V1 and that at x = -5 is V2, then V1 - V2 (in volt) is:

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Q. The electric field in a region is given by $\vec{E} = \left(Ax + B\right)\hat{i}$ where $E$ is in $NC^{-1}$and $x$ is in metres. The values of constants are $A \,= \,20 SI$ unit and $B \,= \,10 SI$ unit. If the potential at $x = 1$ is $V_{1}$ and that at $x = -5$ is $V_{2}$, then $V_{1} - V_{2}$ (in volt) is:

Electrostatic Potential and Capacitance

Solution:

Given, $\vec{E}=(A x+B) \hat{i}$
or $E=20 x+10$
Using $V=\int E d x$, we have
$ V_{2}-V_{1}=\int_{-5}^{1}(20 x+10) d x=-180 V $
or $V_{1}-V_{2}=180 V$