.8 A graph of the x component of the electric field as a function of x in a regi

Question

.8 A graph of the x component of the electric field as a function of x in a region of space is shown. The scale of the vertical axis is set by Es 20.0 N/C. The yand z components of the electric field are zero in this region. If the electric potential at the origin is 10 V (a) what is the electric potential at x= 2.0 m (30 V) (b) what is the greatest positive value of the electric potential for 45 points on the x axis for which 0 s xs 6.0 m (40 V) (c) for what value of xis the electric potential zero? (5.5 m) -E x (m)

Explanation / Answer

Given,

v0 = 10 V ; E = 20 N/C

a)we know that,

E = V/d => V = Ed

So the area Under the graph will be the required value of potential at x = 2

Vx = Vx + V0 = 1/2 x 2 x 20 + 10 = 30 V

Hence, Vx = 30 V

b)In this case

Vx = 1/2 x 3 x 20 + 10 = 40 V

Hence, Vx = 40 V

c)For this,

1/2 x 1 x 20 + (x - 4) x 20 = 40

20 x = 40 + 70 => x = 5.5

Hence, x = 5.5 m

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