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 the charges, and $r$ is the distance between them. We only compare magnitudes.

Step2: Measure distance for each sketch

• Sketch 1 (top-left): Charges +2, -1, distance $r_1=1$ grid unit
• Sketch 2 (top-right): Charges +2, -1, distance $r_2=2$ grid units
• Sketch 3 (bottom-left): Charges +3, -1, distance $r_3=1$ grid unit
• Sketch 4 (bottom-right): Charges +1, -1, distance $r_4=2$ grid units

Step3: Calculate force magnitude for each

• Sketch1: $F_1 = k\frac{|2 \times (-1)|}{1^2}=2k$
• Sketch2: $F_2 = k\frac{|2 \times (-1)|}{2^2}=\frac{2k}{4}=0.5k$
• Sketch3: $F_3 = k\frac{|3 \times (-1)|}{1^2}=3k$
• Sketch4: $F_4 = k\frac{|1 \times (-1)|}{2^2}=\frac{1k}{4}=0.25k$

Step4: Rank forces from strongest to weakest

Order of forces: $F_3 > F_1 > F_2 > F_4$

Answer:

1. (Strongest) - Bottom-left sketch (+3 and -1, distance 1 unit)
2. - Top-left sketch (+2 and -1, distance 1 unit)
3. - Top-right sketch (+2 and -1, distance 2 units)
4. (Weakest) - Bottom-right sketch (+1 and -1, distance 2 units)