The diagram below shows electric field lines | vedclass

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(B) The electric field $E$ is related to the potential $V$ by the relation $E = -\frac{dV}{dx}$.This implies that the magnitude of the electric field

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(B) The electric field $E$ is related to the potential $V$ by the relation $E = -\frac{dV}{dx}$.This implies that the magnitude of the electric field is equal to the magnitude of the potential gradient,$|E| = |\frac{dV}{dx}|$.In the given diagram,the electric field lines are closer together near $X$ and become more spread out (uniform) as we move towards $Y$.This indicates that the electric field strength $|E|$ is higher near $X$ and decreases as we move towards $Y$.Since $|E| = |\frac{dV}{dx}|$,the slope of the potential $V$ versus distance $d$ graph must be steeper near $X$ and become less steep as we move towards $Y$.Among the given options,the graph in option $B$ shows a steep decrease in $V$ near $X$ (high slope) and a shallower decrease as we move towards $Y$ (lower slope),which correctly represents the variation of potential.

The diagram below shows electric field lines in a region of space. Which of the following diagrams best shows the variation with distance $d$ of the potential $V$ along the line $XY$ as we move from $X$ to $Y$?

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