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  4. The electric field in a region is given by vecE = (Ax + B) hati , 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 V1 and that at x = -5 is V2, then V1 - V2 is :-

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Q. The electric field in a region is given by $\vec{E} = (Ax + B)\hat{i}$ , 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 $V_1 - V_2$ is :-

JEE MainJEE Main 2019Electrostatic Potential and Capacitance

Solution:

$\vec{E} = \left(20x +10\right)\hat{i} $
$ V_{1} -V_{2} - \int^{1}_{-5} \left(20x+10\right)dx $
$V_{1} - V_{2} = -\left(10x^{2} + 10x\right)^{1}_{-5}$
$ V_{1} - V_{2} = 10\left(25 - 5 - 1 - 1\right) $
$V_{1} - V_{2} = 180 \,V $