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 x-component of the electric field is given by the negative gradient of the electric potential, i.e. 
E_x = -dV/dx. 
From the graph, we can see that the slope of the potential is positive from x = -2 to x = 0, and negative from x = 0 to x = 2. Therefore, the x-component of the electric field is positive from x = -2 to x = 0, and negative from x = 0 to x = 2. Thus, choice B is the correct answer.

The Graph in the Figure Shows the Variation of the Electric