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A point charge q1 = +2 microcoulomb is fixed at the origin and a…
Question
A point charge q1 = +2 microcoulomb is fixed at the origin and a point charge q2 = -3 microcoulomb is fixed at x = +0.40 m on the x-axis. There is a point on the x-axis at which the net electric field is exactly zero. This null point lies to the left of q1 (x < 0). Find its distance from q1, in metres, to three decimal places.
✓ Verified answer: 1.78checked by our engine — not a guess
Step-by-step solution
The null point cannot lie between the charges (fields add there) and must be nearer the smaller-magnitude charge, hence to the left of q1.
Let its distance from q1 be d; its distance from q2 is (d+0.4).
Setting field magnitudes equal: k|q1|/d^2 = k|q2|/(d+0.4)^2, i.e.
2/d^2 = 3/(d+0.4)^2.
Taking square roots: sqrt(2)(d+0.4) = sqrt(3) d, so d(sqrt(3)-sqrt(2)) = 0.4 sqrt(2), giving d = 0.4 sqrt(2)/(sqrt(3)-sqrt(2)) ≈ 1.780 m.
Final answer1.780
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