In part (a) of the figure, particle 1 (of charge q1) and particle 2 (of charge q

Question

In part (a) of the figure, particle 1 (of charge q1) and particle 2 (of charge q2) are fixed in place on an x axis, 20.00 cm apart. Particle 3 (of charge q3 = +8.00 × 10-19 C) is to be placed on the line between particles 1 and 2 so that they produce a net electrostatic force on it. In part (b) of the figure below gives the x component of that force versus the coordinate x at which particle 3 is placed. The scale of the x axis is set by xs = 20.00 cm. What are (a) the sign of charge q1 and (b) the ratio q2/q1?

Explanation / Answer

At x = 5 cm, the force on q3 is zero. If we move the charge to the left from x = 5 cm, there is an net force to the right (in the x-direction). It indicates that q1 repels q3 and since q3 is positive, q1 is also positively charged. If we move charge to the right from x = 5 cm, there is a net force to the left which again shows that q2 is positively charged.

Place the charge q3 at x = 5 cm
Force on q3 due to q1 = 1/4o [(q1 x q3) / x2]
Force on q3 due to q2 = 1/4o [(q2 x q3) / (20 - x)2]
At x = 5 cm, these two forces cancel each other,
1/4o [(q1 x q3) / x2] = 1/4o [(q2 x q3) / (20 - x)2]
q2/q1 = [(20 - 5)/5]2 = 9

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