Gauss' theorem

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Formula: A = A · n̂ Meaning: The area vector has magnitude equal to the area and direction along the outward normal. Unit: m² for area magnitude. Quick example: For a plane surface, the vector points …

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Given: E = 20 N/C, A = 5 m², θ = 60° Formula: Φ_E = EA cosθ Step 1: cos 60° = 1/2 Step 2: Φ_E = 20 × 5 × (1/2) N·m²/C Step 3: Φ_E = 50 N·m²/C Answer: 50 N·m²/C…

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For a plane surface parallel to the field, θ = 90°. Formula: Φ_E = EA cosθ Since cos 90° = 0, the flux is 0. Physical meaning: field lines do not pass through the surface normally. Example: A surface …

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Definition: Φ_E = ∫ E · dA for an open surface, and Φ_E = ∮ E · dA for a closed surface. Meaning: Electric flux is a measure of the number of field lines passing through a surface. SI unit: N·m²/C or …

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Given: q = 3 μC = 3 × 10^-6 C Formula: Φ_E = q/ε₀ Take ε₀ ≈ 8.85 × 10^-12 C² N^-1 m^-2 Step 1: Φ_E = (3 × 10^-6)/(8.85 × 10^-12) N·m²/C Step 2: Φ_E ≈ 3.39 × 10^5 N·m²/C Answer: 3.39 × 10^5 N·m²/C…

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Formula: Φ_E = ∮ E · dA = q/ε₀ Meaning: The net electric flux through any closed surface equals 1/ε₀ times the net charge enclosed. Condition: It applies to a closed surface. Quick example: If enclose…

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Given: q = 2 μC = 2 × 10^-6 C Formula: Φ_E = q/ε₀ Step 1: Φ_E = (2 × 10^-6)/(8.85 × 10^-12) N·m²/C Step 2: Φ_E ≈ 2.26 × 10^5 N·m²/C Answer: 2.26 × 10^5 N·m²/C…

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A charge outside the surface sends field lines into the surface at one part and out at another part. The inward and outward contributions cancel in the total flux. So, the net flux due to charge outsi…