In a region,the electric field is (30 hat{i} | vedclass

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(D) Given: $\vec{E} = (30 \hat{i} + 40 \hat{j}) 	ext{ NC}^{-1}$ and $V(0,0) = 0 	ext{ V}$.We know that the relation between electric field and elect

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-$110$ $V$

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(D) Given: $\vec{E} = (30 \hat{i} + 40 \hat{j}) 	ext{ NC}^{-1}$ and $V(0,0) = 0 	ext{ V}$.We know that the relation between electric field and electric potential is given by $dV = -\vec{E} \cdot d\vec{r}$.Here,$d\vec{r} = dx \hat{i} + dy \hat{j} + dz \hat{k}$.Integrating from the origin $(0,0)$ to the point $(1,2)$:$\int_{V(0,0)}^{V(1,2)} dV = -\int_{(0,0)}^{(1,2)} (30 \hat{i} + 40 \hat{j}) \cdot (dx \hat{i} + dy \hat{j})$$V(1,2) - V(0,0) = -\left[ \int_{0}^{1} 30 dx + \int_{0}^{2} 40 dy ight]$$V(1,2) - 0 = -[30(1) + 40(2)]$$V(1,2) = -(30 + 80) = -110 	ext{ V}$.

In a region,the electric field is $(30 \hat{i} + 40 \hat{j}) \text{ NC}^{-1}$. If the electric potential at the origin is zero,the electric potential at the point $(1 \text{ m}, 2 \text{ m})$ is

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