Question

Two electrically charged particles in close proximity to one another have electrical potential energy. The amount of energy is dependent on the charges of the particles and the distance between the particles.

The table below shows the positions of two particles relative to each other. The particles have the same charge.

Position Number Distance Between Particle 1
& Particle 2 (in mm)
1 2
2 4
3 6
4 8


At which position do the particles have the greatest electrical potential energy?
A.
position 4
B.
position 3
C.
position 1
D.
position 2

Answer 1

The electrical potential energy (U) between two charged particles is given by the formula:

\[ U = k \frac{q_1 q_2}{r} \]

where:
- \( U \) is the electrical potential energy,
- \( k \) is Coulomb's constant,
- \( q_1 \) and \( q_2 \) are the magnitudes of the charges of the particles, and
- \( r \) is the distance between the charges.

Since the particles have the same charge, \( q_1 \) and \( q_2 \) are constant, and the relationship shows that the potential energy is inversely proportional to the distance \( r \). This means that as the distance between the two particles increases, the potential energy decreases.

Given the distances in the table, the potential energy will be greatest when the distance \( r \) is smallest.

- Position 1: 2 mm (greatest potential energy)
- Position 2: 4 mm
- Position 3: 6 mm
- Position 4: 8 mm (smallest potential energy)

Therefore, the correct answer is **C. position 1**.