The electric potential for an electric field | vedclass

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Question

(A) The relation between electric field $E$ and electric potential $V$ is given by $E = -\frac{dV}{dx}$.This means the electric field is the negative

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(A) The relation between electric field $E$ and electric potential $V$ is given by $E = -\frac{dV}{dx}$.This means the electric field is the negative of the slope of the $V-X$ graph.$1$. For the interval $X \in [-4, -2]$: The slope is $\frac{10 - 0}{-2 - (-4)} = \frac{10}{2} = 5$. Thus, $E = -5$.$2$. For the interval $X \in [-2, 2]$: The potential is constant $(V = 10)$, so the slope is $0$. Thus, $E = 0$.$3$. For the interval $X \in [2, 7]$: The slope is $\frac{0 - 10}{7 - 2} = \frac{-10}{5} = -2$. Thus, $E = -(-2) = 2$.Comparing these values with the given options, option $A$ represents $E = -5$ for $X \in [-4, -2]$, $E = 0$ for $X \in [-2, 2]$, and $E = 2$ for $X \in [2, 7]$.

The electric potential for an electric field directed parallel to $X$-axis is shown in the figure. Choose the correct plot of electric field strength.

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