The graph in the figure shows the variation of the electric potential V(x)(in arbitrary units)as a function of the position x (also in arbitrary units).Which of the choices below correctly describes the orientation of the x-component of the electric field along the x-axis? A) E_x is positive from x = -2 to x = 2. B) E_x is positive from x = -2 to x = 0, and negative from x = 0 to x = 2. C) E_x is negative from x = -2 to x = 0, and positive from x = 0 to x = 2. D) E_x is negative from x = -2 to x = 2.

Question

Quizplus · Accepted Answer

The electric field is the negative of the derivative of the electric potential, i.e., E = -dV/dx. From the graph, we can see that V(x) is increasing from x=-2 to x=0, and decreasing from x=0 to x=2. Therefore, the slope of V(x) is positive from x=-2 to x=0, and negative from x=0 to x=2. Therefore, the derivative dV/dx is positive from x=-2 to x=0, and negative from x=0 to x=2. Therefore, the x-component of the electric field E_x is positive from x=-2 to x=0, and negative from x=0 to x=2. Hence, the correct choice is B.

The Graph in the Figure Shows the Variation of the Electric