Rank the potential energies of the four systems of particles shown in the figure from largest to smallest. Include equalities if appropriate. -Q 1. c>a>b= d 2. b>c=d> a b 3. d>a>c> b 4. a>b=d>c -20 2r 2r 2.

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Chapter1: Units, Trigonometry. And Vectors
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**Rank the potential energies of the four systems of particles shown in the figure from largest to smallest. Include equalities if appropriate.**

Systems (a) through (d) are illustrated, each consisting of pairs of charged particles. The charges are represented as follows:

- **System (a):** Consists of two particles with charges \( Q \) and \( 2Q \) separated by a distance \( r \).
- **System (b):** Consists of two particles with charges \( -Q \) and \( -Q \) separated by a distance \( r \).
- **System (c):** Consists of two particles with charges \( Q \) and \( -Q \) separated by a distance \( 2r \).
- **System (d):** Consists of two particles with charges \( -Q \) and \( -2Q \) separated by a distance \( 2r \).

**Options for ranking:**

1. \( c > a > b = d \)
2. \( b > c = d > a \)
3. \( d > a \geq c > b \)
4. \( a > b = d > c \)
Transcribed Image Text:**Rank the potential energies of the four systems of particles shown in the figure from largest to smallest. Include equalities if appropriate.** Systems (a) through (d) are illustrated, each consisting of pairs of charged particles. The charges are represented as follows: - **System (a):** Consists of two particles with charges \( Q \) and \( 2Q \) separated by a distance \( r \). - **System (b):** Consists of two particles with charges \( -Q \) and \( -Q \) separated by a distance \( r \). - **System (c):** Consists of two particles with charges \( Q \) and \( -Q \) separated by a distance \( 2r \). - **System (d):** Consists of two particles with charges \( -Q \) and \( -2Q \) separated by a distance \( 2r \). **Options for ranking:** 1. \( c > a > b = d \) 2. \( b > c = d > a \) 3. \( d > a \geq c > b \) 4. \( a > b = d > c \)
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