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  4. A uniform electric field of 100 NC- 1 exists in XY plane making an angle 60° with +X direction. Consider points A(.1,2,3.)m and B(.3,2,1.)m then VA-VB is:-

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Q. A uniform electric field of $100\,NC^{- 1}$ exists in $XY$ plane making an angle $60^\circ $ with $+X$ direction. Consider points $A\left(\right.1,2,3\left.\right)m$ and $B\left(\right.3,2,1\left.\right)m$ then $V_{A}-V_{B}$ is:-

NTA AbhyasNTA Abhyas 2022

Solution:

$\vec{E}=100cos60^\circ \hat{i}+100sin60^\circ \hat{j}$
$\vec{E}=50\hat{i}+50\sqrt{3}\hat{j}$
$V_{ A }-V_{ B }=\vec{E} \cdot\left(\vec{r} B -\vec{r}_{ A }\right)$
$=\left(\right.50\hat{i}+50\sqrt{3}\hat{j}\left.\right)\cdot \left(\right.2\hat{i}-2\hat{k}\left.\right)$
$=100$ volt