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

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

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Knight Calc 5th Edition

Ch 23: The Electric Field

문제 34

23장, 문제 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?

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

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.

관련 실천

교과서 질문

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교과서 질문

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교과서 질문

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교과서 질문

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교과서 질문

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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?

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

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?