Question

PH 132 written HW #1 (Coulomb's Force Law): Due 01/25/2019 Particles 1 and 2 have equal charge, Q and are on the y axis at distance d from the origin as shown in the figure below. Particle 3 of charge Qs is located on the x axis. Let's call this position x. A) Find a model for the clectrostatic force acting on the third charge. (8 pts.) B) At what values of x will the magnitude of the electrostatic force on the third particle from the other C) D) two particles be minimum? (2 pt.) At what values of x will the magnitude of the electrostatic force on the third particle from the other two particles be maximum? (6 pts.) Sketch a plot of the force vs. x position. (4 pts.)

Answer 1

Assuming Q_3 is positive Force on Q_3 due Q at position 1 = KQ/d^2 [Cos theta i^^- Sinn theta j^^] F_1 = KQ/d^2 + x^2 [Cos theta i^^- Sin theta j^^] Force on Q_3 due to Q at position 2 r^2 = d^2 + x^2 F_2 = KQ/d^2 + x^2 [Cos theta i^^+ Sin theta j^^] Total Force F = F_1 + F_2 = 2 KQ/d^2 + x^2 Cos theta F = 2KQ x/(d^2 + x^2)3/2 Cos theta = x/r = x/squareroot d^2 + x^2 B, C) For maximum and minimum forces dF/dx = 0 (d^2 + x^2)^3/2 - (3x_2) (d^2 + x^2)^1/2 (2x) = 0 d^2 + x^2 - 3x^2 = 0 d^2 = 2x^2 x = d/squareroot 2, -d/squareroot 2 d^2F/dx^2 = 0 at -d/squareroot 2 Therefore maximum minimum force = 2KQ (-Q/squareroot 2)/(d^2 + d^2/2)^3/2 = -squareroot 2 KQ d/(3d^2/2)^3/2 = -4 KQ d/3 squareroot 3 d^2 maximum force = 2 KQ (d/squareroot 2)