The permanent electric dipole moment of the water molecule (H2O) is 6.2×10−306.2\$$times10^{-30} Cm. $$What is the maximum possible torque on a water molecule in a 5.0×$$1085.0×10^8 N/C $$electric field?

Ch 23: The Electric Field

Knight Calc - Physics for Scientists and Engineers 5th Edition

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Knight Calc 5th Edition

Ch 23: The Electric Field

Problem 34

Chapter 23, Problem 34

The permanent electric dipole moment of the water molecule (H₂O) is $6.2 \times 10^{- 30}$ Cm. What is the maximum possible torque on a water molecule in a $5.0 \times 10^{8}$ N/C electric field?

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Understand the problem: The torque (τ) on a dipole in an electric field is given by the formula τ = pE sin(θ), where p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the electric field. The maximum torque occurs when sin(θ) = 1, i.e., when θ = 90°.

Identify the given values: The dipole moment of the water molecule is p = 6.2×10^−30 C·m, and the electric field strength is E = 5.0×10^8 N/C.

Substitute the given values into the formula for torque: τ = pE. Since sin(θ) = 1 for maximum torque, the formula simplifies to τ = (6.2×10^−30 C·m) × (5.0×10^8 N/C).

Perform the multiplication of the dipole moment and the electric field strength to calculate the maximum torque. Ensure the units are consistent (C·m × N/C = N·m, which is the unit of torque).

Interpret the result: The calculated torque represents the maximum rotational force experienced by the water molecule in the given electric field when the dipole is perpendicular to the field.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Electric Dipole Moment

The electric dipole moment is a measure of the separation of positive and negative charges in a system. It is defined as the product of the charge and the distance between the charges. For a molecule like water, which has a permanent dipole due to its molecular structure, the dipole moment indicates how strongly the molecule can interact with an external electric field.

Torque on a Dipole in an Electric Field

When an electric dipole is placed in an external electric field, it experiences a torque that tends to align it with the field. The torque ( au) can be calculated using the formula τ = pE sin(θ), where p is the dipole moment, E is the electric field strength, and θ is the angle between the dipole moment and the electric field direction. The maximum torque occurs when θ is 90 degrees, simplifying the equation to τ_max = pE.

Electric Field Strength

Electric field strength (E) is a measure of the force per unit charge experienced by a positive test charge placed in the field. It is expressed in newtons per coulomb (N/C). In this context, the electric field strength influences the torque experienced by the water molecule's dipole moment, determining how effectively the molecule can be oriented by the field.

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The permanent electric dipole moment of the water molecule (H2O) is 6.2×10−306.2\(\times\)10^{-30} Cm. What is the maximum possible torque on a water molecule in a 5.0×1085.0×10^8 N/C electric field?

Verified video answer for a similar problem:

Key Concepts

Electric Dipole Moment

Torque on a Dipole in an Electric Field

Electric Field Strength

The permanent electric dipole moment of the water molecule (H₂O) is $6.2 \times 10^{- 30}$ Cm. What is the maximum possible torque on a water molecule in a $5.0 \times 10^{8}$ N/C electric field?