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Question 1.5.6: A system of three electric charges lying in a straight line ...

A system of three electric charges lying in a straight line is in equilibrium. Two of the charges are positive with magnitudes Q and 2Q, and are 50 cm apart. Determine the sign, magnitude and position of the third charge.

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Let Q_{3} be the third change located at the distance x. From Q

V_{1}=\frac{2 Q}{4 \pi E(50)}+\frac{Q_{3}}{4 \pi E(x)}                                      (1)

V_{2}=\frac{Q}{4 \pi E(50)}+\frac{Q_{3}}{4 \pi E(x-50)}                                          (2)

1.6

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