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

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

Step2: Analyze each sketch

• First sketch: \(q_1 = 1\), \(q_2=1\), assume \(r = 4\) (counting grid - squares as units). Then \(F_1=k\frac{1\times1}{4^2}=k\frac{1}{16}\).
• Second sketch: \(q_1 = 2\), \(q_2 = 1\), assume \(r = 3\). Then \(F_2=k\frac{2\times1}{3^2}=k\frac{2}{9}\).
• Third sketch: \(q_1 = 1\), \(q_2 = 3\), assume \(r = 2\). Then \(F_3=k\frac{1\times3}{2^2}=k\frac{3}{4}\).
• Fourth sketch: \(q_1 = 2\), \(q_2 = 1\), assume \(r = 5\). Then \(F_4=k\frac{2\times1}{5^2}=k\frac{2}{25}\).

Step3: Compare the magnitudes of the forces

We have \(F_3 = k\frac{3}{4}\approx0.75k\), \(F_2=k\frac{2}{9}\approx0.22k\), \(F_1 = k\frac{1}{16}= 0.0625k\), \(F_4=k\frac{2}{25}=0.08k\).

Since \(0.75k>0.22k > 0.08k>0.0625k\), the order from strongest to weakest force is: third sketch (\(1\)), second sketch (\(2\)), fourth sketch (\(3\)), first sketch (\(4\)).

Answer:

Third sketch: \(1\) (strongest); Second sketch: \(2\); Fourth sketch: \(3\); First sketch: \(4\) (weakest)