Point charge q1 = +2.0 C is placed at x1 = 0 along the x axis. A second point ch

Question

Point charge q1 = +2.0 C is placed at x1 = 0 along the x axis. A second point charge q2 = -4.0 C is placed at x2 = 10 cm. Initially, q1 and q2 are fixed in their positions by restraints. a) At what position on the x axis can a third point charge, q3, be placed so the third charge will be in equilibrium? (x3 = ? so that q3 is in static equilibrium). b) Does the sign of the charge on q3 or amount of charge on q3 affect the equilibrium of q3 when it is located at this point? (Yes or No) c) If the charge on q3 is chosen correctly, then both q1 and q2 will also be in equilibrium when q3 is placed at x3 and the restraints on q1 and q2 can be released. What charge must q3 have so that both q1 and q2 are in equilibrium? (Specify both the magnitude and the sign of the charge on q3.)

Explanation / Answer

(a) At a distance on the x-axis, a third point charge be placed which can given as :

E1 = - E2

ke q1 / x2 = - ke q1 / (0.1 - x)2

(2 x 10-6 C) / x2 = (4 x 10-6 C) / (0.1 - x)2

2 (0.1 - x)2 = 4 x2

2 [(0.01) - (0.2)x + x2 = 4 x2

(0.02) - (0.4) x = 3 x2

3 x2 + (0.4) x - (0.02) = 0

it's an quadratic equation and we get -

x = - 0.172 m         or        x = 0.038 m

(b) Yes, the sign of the charge on q3 or amount of charge on q3 affect the equilibrium of q3 when it is located at this point.

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