Question

Two particles with charges q₁ and q₂ are separated by distance d. Rank these scenarios according to the magnitude of the electrostatic (coulombic) potential energy. Ignore sign.

A. q₁= +1, q₂= -1, d= 3Å
B. q₁= +1, q₂= -1, d= 1Å
C. q₁= +4, q₂= -4, d= 4Å

Answer 1

The electrostatic potential energy can be ranked from lowest to highest magnitude by calculating the potential energy for each scenario using the given values and formula.

Step-by-step explanation:

In order to rank the scenarios according to the magnitude of the electrostatic potential energy, we need to consider the formula for electrostatic potential energy. The formula is given by:

PE = k(q₁)(q₂)/d

Where:

• PE is the electrostatic potential energy
• k is the electrostatic constant (k = 9 x 10^9 Nm²/C²)
• q₁ and q₂ are the charges of the particles
• d is the distance between the particles

Using the given values, we can calculate the potential energy for each scenario:

1. A: PE = (9 x 10^9 Nm²/C²)(+1)(-1)/(3 x 10^-10 m) ≈ -3 x 10^-19 J
2. B: PE = (9 x 10^9 Nm²/C²)(+1)(-1)/(1 x 10^-10 m) ≈ -9 x 10^-19 J
3. C: PE = (9 x 10^9 Nm²/C²)(+4)(-4)/(4 x 10^-10 m) ≈ -9 x 10^-19 J

Based on these calculations, we can rank the scenarios from lowest to highest magnitude of electrostatic potential energy as follows:

1. C
2. B
3. A