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3. Four positive and four negative charges of equal magnitudes +Q are arranged alternately on the corners of a cube of side length d, +Q as drawn. This is a model of one cell of an ionic crystal such as -Q +Q salt, NaCl. a. Calculate the potential energy of this configuration. As usual, take the energy to be zero infinitely far away from the charges. Express the energy in terms of k, Q, and d. -Q d. Hints: -Q +Q There are 12 pairs of opposite charges along the edges There are 12 pairs of like charges along the diagonals of each face There are 4 pairs of opposite charges along the cube's long diagonals

3. Four positive and four negative charges of equal magnitudes +Q are arranged alternately on the corners of a cube of side length d, +Q as drawn. This is a model of one cell of an ionic crystal such as -Q +Q salt, NaCl. a. Calculate the potential energy of this configuration. As usual, take the energy to be zero infinitely far away from the charges. Express the energy in terms of k, Q, and d. -Q d. Hints: -Q +Q There are 12 pairs of opposite charges along the edges There are 12 pairs of like charges along the diagonals of each face There are 4 pairs of opposite charges along the cube's long diagonals

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Electric Potential Energy (An lonic Crystal) 3. Four positive and four negative charges of equal magnitudes +Q are arranged alternately on the corners of a cube of side length d, +Q as drawn. This is a model of one cell of an ionic crystal such as -Q +Q salt, NaCl. a. Calculate the potential energy of this configuration. As d usual, take the energy to be zero infinitely far away from the charges. Express the energy in terms of k, Q, and d. d Hints: -Q +Q There are 12 pairs of opposite charges along the edges There are 12 pairs of like charges along the diagonals of each face There are 4 pairs of opposite charges along the cube's long diagonals b. In part (a), you should have determined that U < 0. Explain the relationship between this result and the observation that such crystals freely form in nature.
Transcribed Image Text:Electric Potential Energy (An lonic Crystal) 3. Four positive and four negative charges of equal magnitudes +Q are arranged alternately on the corners of a cube of side length d, +Q as drawn. This is a model of one cell of an ionic crystal such as -Q +Q salt, NaCl. a. Calculate the potential energy of this configuration. As d usual, take the energy to be zero infinitely far away from the charges. Express the energy in terms of k, Q, and d. d Hints: -Q +Q There are 12 pairs of opposite charges along the edges There are 12 pairs of like charges along the diagonals of each face There are 4 pairs of opposite charges along the cube's long diagonals b. In part (a), you should have determined that U < 0. Explain the relationship between this result and the observation that such crystals freely form in nature.
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