Two point charges are placed on the x -axis. The charge +2 q is at x = 1.5 m, an

Question

Two point charges are placed on the x-axis. The charge +2q is at x = 1.5 m, and the charge q is at x = 1.5 m.

(a) There is a point on the x-axis between the two charges where the electric potential is zero. Where is this point? (Answer in m)

(b) The electric potential also vanishes in one of the following regions. Identify the appropriate region.

1) Region 1: 5.0 m > x > 1.5 m

2) Region 2: 1.5 m > x > 3.0 m     

3) Region 3: 3.5 m > x > 5.0 m

(c) Find the value of x referred to in part (b). (Answer in m)

Explanation / Answer

d = distance between the two charges = 1.5 m + 1.5 m = 3 m

q1 = charge on right side of origin = 2 q

q2 = charge on left side of origin = - q

a)

let the Electric potential be 0 at distance 'd' from charge 'q2'

Electric potential by charge q2

V2 = k q2 /d = - k q/d

Electric potential by charge q1

V1 = k q1 /(3 - d) = 2k q/(3 - d)

V1 + V2 =0

(- k q/d) + (2k q/(3 - d)) = 0

k q/d = 2k q/(3 - d)

3 - d = 2 d

d = 1 m

so point is at X = - 1.5 + 1 = - 0.5 m

b)

Region 3: 3.5 m > x > 5.0 m

c)

when the point of zero potential is to the left of charge 'q2' at distance 'd'

Electric potential by charge q2

V2 = k q2 /d = - k q/d

Electric potential by charge q1

V1 = k q1 /(3 + d) = 2k q/(3 + d)

V1 + V2 =0

(- k q/d) + (2k q/(3 + d)) = 0

3 + d = 2 d

d = 3 m

so X = - 3 -1.5 = - 4.5

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