Question

your answer is incorrect. decide how the sketches below would be listed, if they were listed in order of decreasing force between the charges. that is, select \1\ beside the sketch with the strongest force between the charges, select \2\ beside the sketch with the next strongest force between the charges, and so on. note for advanced students: since the units of each charge are not written, you may assume any convenient and reasonable unit, for example coulombs or multiples of e.

Explanation:

Step1: Recall Coulomb's Law

Coulomb's Law is $F = k\frac{\vert q_1q_2\vert}{r^{2}}$, where $k$ is a constant, $q_1$ and $q_2$ are the charges, and $r$ is the distance between the charges.

Step2: Analyze each sketch

• First sketch: $\vert q_1q_2\vert=\vert(- 2)\times(+1)\vert = 2$, assume distance $r_1 = 2$ units. Then $F_1=k\frac{2}{2^{2}}=\frac{k}{2}$.
• Second sketch: $\vert q_1q_2\vert=\vert(-2)\times(+1)\vert = 2$, assume distance $r_2 = 3$ units. Then $F_2=k\frac{2}{3^{2}}=\frac{2k}{9}$.
• Third sketch: $\vert q_1q_2\vert=\vert(+1)\times(-1)\vert = 1$, assume distance $r_3 = 2$ units. Then $F_3=k\frac{1}{2^{2}}=\frac{k}{4}$.
• Fourth sketch: $\vert q_1q_2\vert=\vert(+1)\times(-1)\vert = 1$, assume distance $r_4 = 3$ units. Then $F_4=k\frac{1}{3^{2}}=\frac{k}{9}$.

Step3: Compare the magnitudes of the forces

Since $\frac{k}{2}>\frac{2k}{9}>\frac{k}{4}>\frac{k}{9}$, the order of forces from strongest to weakest is: First sketch ($1$), Second sketch ($2$), Third sketch ($3$), Fourth sketch ($4$).

Answer:

First sketch: $1$ (strongest), Second sketch: $2$, Third sketch: $3$, Fourth sketch: $4$ (weakest)