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Ch 22: Gauss' Law
Young & Freedman Calc - University Physics 14th Edition
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Young & Freedman Calc 14th EditionCh 22: Gauss' Law문제 26a
22장, 문제 26a

A very large, horizontal, nonconducting sheet of charge has uniform charge per unit area σ=5.00×10−6\(\sigma\)=5.00\(\times\)10^{-6} C/m2. A small sphere of mass m=8.00×10−6m=8.00\(\times\)10^{-6} kg and charge qq is placed 3.00 3.00 cm above the sheet of charge and then released from rest. If the sphere is to remain motionless when it is released, what must be the value of qq?

검증된 단계별 안내
1
Understand the problem: We have a charged sheet and a charged sphere. The sphere is released from rest and should remain motionless. This implies that the forces acting on the sphere must be balanced.
Identify the forces: The sphere experiences two forces: the gravitational force pulling it downward and the electric force due to the charged sheet pushing it upward.
Calculate the gravitational force: The gravitational force \( F_{gravity} \) acting on the sphere is given by \( F_{gravity} = m \cdot g \), where \( m \) is the mass of the sphere and \( g \) is the acceleration due to gravity (approximately \( 9.81 \text{ m/s}^2 \)).
Calculate the electric force: The electric field \( E \) due to a large sheet of charge is given by \( E = \frac{\sigma}{2\varepsilon_0} \), where \( \sigma \) is the charge per unit area and \( \varepsilon_0 \) is the permittivity of free space (approximately \( 8.85 \times 10^{-12} \text{ C}^2/\text{N} \cdot \text{m}^2 \)). The electric force \( F_{electric} \) on the sphere is \( F_{electric} = q \cdot E \).
Set the forces equal for equilibrium: For the sphere to remain motionless, the electric force must equal the gravitational force. Therefore, \( q \cdot E = m \cdot g \). Substitute the expression for \( E \) and solve for \( q \): \( q = \frac{m \cdot g}{\frac{\sigma}{2\varepsilon_0}} \).

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
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주요 개념

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

Electric Field of a Charged Sheet

The electric field generated by a large, uniformly charged nonconducting sheet is constant and perpendicular to the sheet. It is given by E = σ / (2ε₀), where σ is the charge density and ε₀ is the permittivity of free space. This field influences the motion of charged objects placed near the sheet.
추천 영상:
가이드 코스
06:28
Electric Field due to a Point Charge

Force Balance

For the sphere to remain motionless, the net force acting on it must be zero. This requires balancing the gravitational force (mg) acting downward with the electric force (qE) acting upward. Solving for q involves equating these forces, ensuring the sphere remains stationary.
추천 영상:
가이드 코스
06:05
Balancing a bar with a force

Gravitational Force

The gravitational force acting on an object is given by F = mg, where m is the mass and g is the acceleration due to gravity (approximately 9.81 m/s² on Earth). This force acts downward and must be counteracted by the electric force for the sphere to remain motionless.
추천 영상:
가이드 코스
05:41
Gravitational Forces in 2D
관련 실천
교과서 질문

Charge qq is distributed uniformly throughout the volume of an insulating sphere of radius R=4.00R = 4.00 cm. At a distance of r=8.00r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude E=940E = 940 N/C. What is the volume charge density for the sphere?

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교과서 질문

A conductor with an inner cavity, like that shown in Fig. 22.2322.23c, carries a total charge of +5.00+5.00 nC. The charge within the cavity, insulated from the conductor, is −6.00−6.00 nC. How much charge is on (a) the inner surface of the conductor and (b) the outer surface of the conductor?

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교과서 질문

An infinitely long cylindrical conductor has radius r r and uniform surface charge density σσ. In terms of σσ, what is the magnitude of the electric field produced by the charged cylinder at a distance r>Rr > R from its axis? Then, express the result in terms of λλ and show that the electric field outside the cylinder is the same as if all the charge were on the axis.

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교과서 질문

A very large, horizontal, nonconducting sheet of charge has uniform charge per unit area σ=5.00×10−6\(\sigma\)=5.00\(\times\)10^{-6} C/m2. A small sphere of mass m=8.00×10−6m=8.00\(\times\)10^{-6} kg and charge qq is placed 3.00 3.00 cm above the sheet of charge and then released from rest. What is qq if the sphere is released 1.501.50 cm above the sheet?

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교과서 질문

Charge qq is distributed uniformly throughout the volume of an insulating sphere of radius R=4.00R = 4.00 cm. At a distance of r=8.00r = 8.00 cm from the center of the sphere, the electric field due to the charge distribution has magnitude E=940E = 940 N/C. What is the electric field at a distance of 2.002.00 cm from the sphere's center?

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교과서 질문

An infinitely long cylindrical conductor has radius r r and uniform surface charge density σσ. In terms of σσ and RR, what is the charge per unit length λλ for the cylinder?

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