The electric field in a region is given by $\vec{E} = (A x + B) \hat{i},$ where E is in $N C^{- 1}$ and x is in meters. 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

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answer is 180.

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Detailed Solution

$\begin{array}{l} V = - \int E d x w e h a v e \\ V_{2} - V_{1} = \int_{- 5}^{1} (20 x + 10) d x = - 180 V \\ \Rightarrow V_{1} - V_{2} = 180 V \end{array}$

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