A charge + q is located at the origin, while an identical charge is located on the x axis at x = + 0.91 m. A third charge of + 3q is located on the x axis at such a place that the net electrostatic force on the charge at the origin doubles, its direction remaining unchanged. Where should the third charge be located?

Question

Physics

Martin Baker

12 January, 08:14

A charge + q is located at the origin, while an identical charge is located on the x axis at x = + 0.91 m. A third charge of + 3q is located on the x axis at such a place that the net electrostatic force on the charge at the origin doubles, its direction remaining unchanged. Where should the third charge be located?

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Answers (1)

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Kenzie Guerra · Answer 1

Charge should be located at x = 0.7071m

Explanation:

We are given;

r = 0.5m

From coulombs law, we know that;

F = k•q1•q2/r²

k is electrostatic constant with a value of 9 x 10^ (9) N. m²/C²

Now force between q and q is;

F1 = 9 x 10^ (9) • (q²) / 0.5² = 3.6 x 10^ (10) q²

Now force between q and 2q is;

F2 = 9 x 10^ (9) • (q x 2q) / r²

F2 = 1.8 x 10^ (10) q²/r

Net force = F1 + F2

F_net = 3.6 x 10^ (10) q² + 1.8 x 10^ (10) q²/r²

To get the required location,

F_net = 2F1

Thus,

3.6 x 10^ (10) q² + 1.8 x 10^ (10) q²/r² = 2 (3.6 x 10^ (10) q²)

Divide through by q² to get;

3.6 x 10^ (10) + (1.8 x 10^ (10)) / r = 2 (3.6 x 10^ (10))

(1.8 x 10^ (10)) / r² = (7.2 x 10^ (10)) - (3.6 x 10^ (10))

(1.8 x 10^ (10)) / r² = 3.6 x 10^ (10)

r² = (1.8 x 10^ (10)) / 3.6 x 10^ (10)

r² = 0.5

r = √0.5

r = 0.7071m