Q 12-02-178JEE MainJEE Main 2019 (8 Apr, Shift 2)Easy
The electric field in a region is given by $\vec E = (Ax + B)\hat i$, where $E$ is in $\text{N C}^{-1}$ 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
Answer: (C) $180\ \text{V}$
$$V_1 - V_2 = -\int_{-5}^{1}(20x + 10)\,dx = -\Big[10x^2 + 10x\Big]_{-5}^{1}$$
$$= -\big[(10 + 10) - (250 - 50)\big] = -(20 - 200) = 180\ \text{V}$$
Solution by Sreeraj P, M.Sc Physics