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

Vedclass · Accepted Answer

$E_{A}=E_{C}$ and $E_{B} < E_{D}$

Vedclass · Answer

(D) The electric field $E$ is related to the potential $V$ by the relation $E = -\frac{dV}{dx}$. The magnitude of the electric field is $|E| = |\frac{dV}{dx}|$,which represents the slope of the $V-x$ graph.In region $A$ ($x=0$ to $1$ m),$V$ is constant ($2$ $V$),so the slope $\frac{dV}{dx} = 0$. Thus,$E_{A} = 0$.In region $B$ ($x=1$ to $2$ m),the slope is $\frac{4-2}{2-1} = 2$ $V$/m. Thus,$|E_{B}| = 2$ $V$/m.In region $C$ ($x=2$ to $4$ m),$V$ is constant ($4$ $V$),so the slope $\frac{dV}{dx} = 0$. Thus,$E_{C} = 0$.In region $D$ ($x=4$ to $5$ m),the slope is $\frac{0-4}{5-4} = -4$ $V$/m. Thus,$|E_{D}| = |-4| = 4$ $V$/m.Comparing the magnitudes: $E_{A} = E_{C} = 0$ and $E_{B} = 2$ $V$/m,$E_{D} = 4$ $V$/m. Therefore,$E_{A} = E_{C}$ and $E_{B} < E_{D}$.

The figure shows the electric potential $V$ as a function of distance through four regions on the $x$-axis. Which of the following is true for the magnitude of the electric field $E$ in these regions?

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