Question

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

The electrostatic force between two charges is given by $$F = k\frac{|q_1 q_2|}{r^2}$$ where $k$ is a constant, $q_1,q_2$ are charge magnitudes, and $r$ is the distance between charges.

Step2: Assign grid units to distance

Let each grid square side = 1 unit. Calculate $r$ and $|q_1 q_2|$ for each sketch:

1. Top-left: $q_1=1, q_2=1, r=4$ → $F \propto \frac{1*1}{4^2} = \frac{1}{16}$
2. Top-right: $q_1=1, q_2=2, r=3$ → $F \propto \frac{1*2}{3^2} = \frac{2}{9} \approx 0.222$
3. Bottom-left: $q_1=2, q_2=1, r=2$ → $F \propto \frac{2*1}{2^2} = \frac{2}{4} = 0.5$
4. Bottom-right: $q_1=2, q_2=1, r=4$ → $F \propto \frac{2*1}{4^2} = \frac{2}{16} = 0.125$

Step3: Rank forces from largest to smallest

Compare proportional values: $0.5 > 0.222 > 0.125 > \frac{1}{16}=0.0625$

Answer:

• Bottom-left sketch: 1 (strongest)
• Top-right sketch: 2
• Bottom-right sketch: 3
• Top-left sketch: 4 (weakest)