Question

Electric fields, please explain answers.

1. Suppose that for these two equally charged pith-balls of mass m 1.0 × 10-4kg hanging from strings of length a-0.25m, θ 10°-π/18rad, what charge q is on each of them? 2. A positive ion of charge q1.6x 10-1C and mass 1.6x 10-23kg is "shot" at initial speed vo 5000m/s into a region containing a strong electric field E = 1000N/CJ of width L = 0.2m used to deflect a beam of such ions. How fast is the ion traveling when it exits the deflector? At what angle θ is its velocity directed upon exit? If it barely "clears" the top plate of the deflector and entered halfway between the plates, how far apart are the deflector plates? 3. What is the total electrostatic potential energy of this collection of three charges on an equilateral triangle? Assume that they have been placed at these locations by bringing them in from "infinity", where their potential energy was zero.

Answer 1

Distance b/w two particles = r = 0.2 times sin theta times 2 = 0.07 m so Fe = k q^2 /r^2 = 9 times 10^9 times q^2 /0.0049 = 1836.7 times 10^9 q^2 Let T be the tension in the string then T cos theta = m g and T sin theta = Fe So tan theta = Fe/mg OR Fe = mg tan theta 1836.7 times 10^9 q^2 = 1.0 times 10^-4 times 9.8 times 0.1763 = 1.728 times 10^-4 q = 1.728 times 10^-4 = 9.7 times 10^-9 c = 1836.7 times 10^9 q = 9.7 times 10^-9 c a_y = q E/m = 1.6 times 10^-19 times 1000/1.6 times 10^-23 = 10^7 m/s^2 delta t = 0.2/5000 = 4 times 10^-5 (s) V_x = 5000 m/s and V_y = 10^7 times 4 times 10^-5 = 400 m/s So v = squareroot V^2_x + V^2_y = 5016 m/s tan theta = V_y /V_x = 0.08 = > theta