Question

1/2 points Three balls, with charges of +4q, -2q, and -q, are equally spaced along a line. The spacing between different ways, as shown in the figure. In each case, the balls are in an isolated region of space very far from anything eise. 2 (a) Rank the three cases, from largest to smallest, based on the magnitude of the net force experienced by the ball with the +4q charge. (Use only "or"symbols. Do not include any parentheses around the letters or symbols.) 1-3>2 (b) If q is 7.80 x 10-6 C and r is 35.0 cm, calculate the magnitude and direction of the net force acting on the ball with the +4q charge in case 1. (Define the positive direction as pointing to the right, so your answer should have a positive sign if the net force is directed right, and a negative sign if the net force is directed left.) 5.15

Answer 1

There is two forces acting on 4q, one due to -2q and the other due to -q, both towards left since, 4q is greater than 2q and q and 4q is positive and other two are negative.

Force acting on 4q is given by,

  $\large F=F(due\, to\,-2q)+F(due\, to\,-q)$

$\large =\frac{k\times4q\times-2q}{r^2}+\frac{k\times4q\times-q}{(2r)^2}$

$\large =\frac{k\times-8q^2}{r^2}+\frac{k\times-4q^2}{4r^2}$

$\large =\frac{k\times-8q^2}{r^2}+\frac{k\times-q^2}{r^2}$

$\large =\frac{kq^2}{r^2} [-8-1]$

$\large =\frac{-9kq^2}{r^2}$

$\large =\frac{-9\times(9\times10^9)\times(7.8\times10^-^6)^2}{(35\times10^-^2)^2}$

= -40.23 N.