FIGURE EX24.18 shows three charges. Draw these charges on your paper four times. Then draw two-dimensional cross sections of three-dimensional closed surfaces through which the electric flux is (a) $2 q divided by epsilon sub 0$ , (b) $q divided by epsilon sub 0$ , (c) 0, and (d) $5 q divided by epsilon sub 0$ .

검증된 단계별 안내

Step 1: Recall Gauss's Law, which states that the electric flux (Φ) through a closed surface is given by Φ = Q_enclosed / ϵ₀, where Q_enclosed is the total charge enclosed by the surface and ϵ₀ is the permittivity of free space. This will guide us in determining the flux for each case.

Step 2: For case (a), where the flux is 2q / ϵ₀, identify a closed surface that encloses a total charge of 2q. Draw a surface (e.g., a sphere or cube) that surrounds two of the charges, ensuring the total enclosed charge sums to 2q.

Step 3: For case (b), where the flux is q / ϵ₀, identify a closed surface that encloses a total charge of q. Draw a surface that surrounds only one of the charges, ensuring the total enclosed charge is q.

Step 4: For case (c), where the flux is 0, identify a closed surface that encloses no net charge. This could be a surface that encloses equal positive and negative charges, resulting in a net charge of 0. Draw such a surface.

Step 5: For case (d), where the flux is 5q / ϵ₀, identify a closed surface that encloses a total charge of 5q. Draw a surface that surrounds all three charges, ensuring the total enclosed charge sums to 5q.

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주요 개념

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

Electric Flux

Electric flux is a measure of the electric field passing through a given area. It is mathematically defined as the product of the electric field (E) and the area (A) through which it passes, adjusted for the angle (θ) between the field lines and the normal to the surface: Φ = E · A · cos(θ). The unit of electric flux is the volt-meter (V·m) or equivalently, newton-meter squared per coulomb (N·m²/C).

Gauss's Law

Gauss's Law states that the total electric flux through a closed surface is proportional to the enclosed electric charge. Mathematically, it is expressed as Φ = Q_enc / ε₀, where Q_enc is the total charge enclosed by the surface and ε₀ is the permittivity of free space. This law is fundamental in electrostatics and simplifies the calculation of electric fields for symmetric charge distributions.

Closed Surfaces in Electrostatics

In electrostatics, a closed surface is an imaginary boundary that completely encloses a volume in space. The choice of this surface is crucial for applying Gauss's Law, as it allows for the determination of the electric field based on the symmetry of the charge distribution. Different configurations of charges will yield different electric flux values through the surface, depending on the amount of charge enclosed.

FIGURE EX24.18 shows three charges. Draw these charges on your paper four times. Then draw two-dimensional cross sections of three-dimensional closed surfaces through which the electric flux is (a) 2q/ϵ02q / ϵ_0, (b) q/ϵ0q / ϵ_0, (c) 0, and (d) 5q/ϵ05q / ϵ_0.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Electric Flux

Gauss's Law

Closed Surfaces in Electrostatics