## College Physics (4th Edition)

We can rank the situations in order of the magnitude of the electric force on $Q_1$, from largest to smallest: $a = b \gt d \gt c = e$
We can write a general expression for the electric force exerted on charge $q_1$: $F = \frac{k~q_1~q_2}{r^2}$ Let $q = 1~\mu C$ Let $r = 1~m$ In each case, we can find an expression for the electric force exerted on charge $Q_1$. (a) $F = \frac{k~Q_1~Q_2}{d^2} = \frac{k~(q)(2q)}{(r)^2} = 2\times \frac{k~q^2}{r^2}$ (b) $F = \frac{k~Q_1~Q_2}{d^2} = \frac{k~(2q)(-1q)}{(r)^2} = -2\times \frac{k~q^2}{r^2}$ (c) $F = \frac{k~Q_1~Q_2}{d^2} = \frac{k~(2q)(-4q)}{(4r)^2} = -\frac{1}{2}\times \frac{k~q^2}{r^2}$ (d) $F = \frac{k~Q_1~Q_2}{d^2} = \frac{k~(-2q)(2q)}{(2r)^2} = -1\times \frac{k~q^2}{r^2}$ (e) $F = \frac{k~Q_1~Q_2}{d^2} = \frac{k~(4q)(-2q)}{(4r)^2} = -\frac{1}{2}\times \frac{k~q^2}{r^2}$ We can rank the situations in order of the magnitude of the electric force on $Q_1$, from largest to smallest: $a = b \gt d \gt c = e$