Two point charges, Q_1 = 3.4 mu C and Q_2 = -2.1 mu C, are placed on the x axis.

Question

Two point charges, Q_1 = 3.4 mu C and Q_2 = -2.1 mu C, are placed on the x axis. Suppose that Q_2 is placed at the origin, and Q_1 is placed at the coordinate x_1 = -6.0 cm (Figure 1). At what point(s) along the axis is the electric field zero? Determine the x-coordinate(s) of the point(s). Express your answer using two significant figures. If there is more than one answer, enter your answers in ascending order separated by commas. At what point(s) along the x axis is the potential zero? Determine the x-coordinate(s) of the point(s). Express your answer using two significant figures. If there is more than one answer, enter your answers in ascending order separated by commas.

Explanation / Answer

a)

Let the point be at distance x from the origin to its right

So, Electric field due to Q1 : E1 = k*Q1/(0.06 + x)^2

and thus electric field due to Q2 : E2 = -k*Q2/x^2

So, Net electric field due to both :

Enet = E1+ E2 = 0

So, k*Q1/(0.06 + x)^2 - k*Q2/x^2 = 0

So, 3.4/(0.06+x)^2 = 2.1/x^2

So, x = +0.22 m <-------- answer

b)

For potential to be 0:

V1 = V2

So, k*Q1/r1 = k*Q2/r2

So, 3.4/r = 2.1/(0.06 - r)

So, r = 0.037 cm (to the right of Q1 )

So, the point is x = -(0.06 - 0.037) = -0.023 m = -2.3 cm

Let another point be at r distance on the left of Q1

So, k*Q1/r = k*Q2/(0.06 + r)

So, 3.4/r = 2.1/(0.06 + r)

So, r = -0.157

So, the point is x = 15.7 - 6 = +11.7 cm

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