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 below. The scale of the vertical axis is set by Exs = 32.5 N/C. The y and z components of the electric field are zero in this region. Suppose that the electric potential at the origin is 16 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?

(c) For what value of x is the electric potential zero?

Explanation / Answer

Exs = 32.5 N/C
V(0) = 16 V

a)

at x =2 m

V(2) = V(0) - area under E-x curve

V(2) = 16 - (-0.5 * 32.5 * 2)

V(2) = 48.5 V

the potential at x = 2 is 48.5 V

b)

as the potential increases in the direction of decreasing electric field

the potential is maximum at x = 2

the greatest value of potential is 48.5 V

c)

for zero potential

let the point is at x

0 = V(0) - (-0.5 * 32.5 * 3 + 0.5 * 32.5 * 1 + 32.5 * (x - 4))

0 = 16 - (-0.5 * 32.5 * 3 + 0.5 * 32.5 * 1 + 32.5 * (x - 4))

solving for x

x = 5.49 m

the potential is zero at x= 5.49 m

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