Question

# Two point charges, Q1 = 3.5 μC and Q2 = -1.5 μC , are placed on...

Two point charges, Q1 = 3.5 μC and Q2 = -1.5 μC , are placed on the x axis. Suppose that Q2 is placed at the origin, and Q1 is placed at the coordinate x1 = − 6.0 cm (Figure 1).

A)At what point(s) along the x axis is the electric field zero? Determine the x-coordinate(s) of the point(s). Show Steps.

Suppose at distance 'd' from charge Q2 net electric field is zero, then

Electric field is given by:

E = kQ/R^2

Since we know that direction of electric field due to +ve charge will be away from charge and due to -ve charge will be towards the charge. In given case since Q1 is +ve and Q2 is -ve, So electric field will be zero towards the right side of Q2 (Since |Q1| > |Q2|)

Enet = E1 - E2 = 0

E1 = E2

kQ1/r1^2 = kQ2/r2^2

Q1 = 3.5 C

Q2 = -1.5 C

r1 = d+ 0.06

r2 = d

Using above values:

Q1/r1^2 = Q2/r2^2

3.5/(d + 0.06)^2 = 1.5/d^2

d/(d + 0.06) = sqrt(1.5/3.5)

d = sqrt(1.5/3.5)*(d + 0.06 )

d = 0.06/(1 - sqrt(1.5/3.5))

d = 0.174 m = 17.4 cm

So electric field will be zero at x = 17.4 cm

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