In the figure below, particles 1 and 2 of charge q1 = q2 = +4 .80 times 10-19 C

Question

In the figure below, particles 1 and 2 of charge q1 = q2 = +4 .80 times 10-19 C are on a y axis at distance d = 21.0 cm from the origin. Particle 3 of charge q3 = +6.40 times 10-19 C is moved gradually along the x axis from x = 0 to x = +5.0 m. At what values of x will the magnitude of the electrostatic force on the third particle from the other two particles be (a) minimum and (b) maximum? What are the (c) minimum and (d) maximum magnitudes? position of minimum force m position of maximum force m magnitude of minimum force N magnitude of maximum force N

Explanation / Answer

When the charge q3 is at x = 0 m then we have F' = F1 - F2 = [k q1 * q3 / d^2 ] - [k q2 * q3 / d^2 ] = [k q3 / d^2 ] * [ q1 - q2] = [ 9 x 10^9 * 6.40 x 10^-19 / 0.21^2] * [0] = 0 N When the charge q3 is at x = 5 m then we have F'' = [F1 + F2] cos45 = [k q1 * q3 / r^2 ] - [k q2 * q3 / r^2 ] cos45 = [k q3 / r^2 ] * [ q1 + q2] * cos45 = [ 9 x 10^9 * 6.40 x 10^-19 / 5.0044^2] * [9.60 x 10^-19] * cos45 = 15.612 x 10^-29 N (a) X = 5 m (b) X = 0 m (c) F'' = 15.612 x 10^-29 (d) F' = 0 N

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