A graph of the x component of the electric field as a function of x in a region

Question

A graph of the x component of the electric field as a function of x in a region of space is shown in the figure. The scale of the vertical axis is set by Exs = 20.0 N/C. The y and z components of the electric field are zero in this region. If the electric potential at the origin is 18 V, (a) what is the electric potential at x = 2.0 m, (b) what is the greatest positive value of the electric potential for points on the x axis for which 0 <= x <= 6.0 m, and (c) for what value of x is the electric potential zero?

Explanation / Answer

V-Vo = -integration (E.ds) from x1 to x2

x1 = 0

x2 = 2

V - 18 = -integration (20.ds) from 0 to 2

V-18 = 2*20/2

V = 38 V

part b )

for any region within 0<x<3 m -integration (E.ds) is positive

but fir any region for which x > 3 is negative

therefore V = Vmax accurs at x = 3 m

Vmax -18 = -integration (E.ds) from 0 to 3

Vmax = 48 V

part c )

for 3 <x <4 and rectange 4 <x <X

1/2 * (1) * 20 + (X-4) * 20 = 48

X = 5.9 m

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