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Multiple Choice
The water molecule is a permanent electric dipole with a dipole moment of . A water molecule is aligned with an electric field of magnitude . How much energy is required to rotate the molecule 180°?
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Verified step by step guidance
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Understand that the energy required to rotate a dipole in an electric field is given by the formula: U = -p * E * cos(θ), where U is the potential energy, p is the dipole moment, E is the electric field, and θ is the angle between the dipole moment and the electric field.
Initially, the water molecule is aligned with the electric field, so the initial angle θ_initial is 0 degrees. The initial potential energy U_initial is -p * E * cos(0) = -p * E.
After rotating the molecule 180 degrees, the angle θ_final becomes 180 degrees. The final potential energy U_final is -p * E * cos(180) = p * E.
The energy required to rotate the molecule is the change in potential energy, which is ΔU = U_final - U_initial.
Substitute the given values into the equation: p = 6.2×10^-30 C·m, E = 7600 V/m, and calculate ΔU = (p * E) - (-p * E) = 2 * p * E to find the energy required for the rotation.