Electromagnetic Induction

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Faraday’s first law: When the magnetic flux through a circuit is changing, an induced emf is set up in the circuit whose magnitude is equal to the negative rate of change of magnetic flux. Formula: e …

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Faraday’s second law: The direction of the induced emf, or the current, in any circuit is such as to oppose the cause that produces it. This is also called Lenz’s law. Meaning: the induced current res…

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Given: N = 100 ΔΦ_B = 0.094 Wb Δt = 10^-3 s Formula: e = -N(ΔΦ_B/Δt) Step 1: magnitude of emf = 100 × (0.094 / 10^-3) V Step 2: = 100 × 94 V Step 3: = 9400 V Answer: magnitude of induced emf = 9400 V.

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Given: e = 31 mV = 31 × 10^-3 V R = 10 Ω Formula: I = e/R Step 1: I = (31 × 10^-3 V) / (10 Ω) Step 2: I = 3.1 × 10^-3 A Step 3: I = 3.1 mA Answer: induced current = 3.1 mA. Unit check: V/Ω = A.

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A faster motion means a larger rate of change of magnetic flux through the coil. From Faraday’s law, e is proportional to dΦ_B/dt, so larger flux change per second gives larger induced emf. If the cir…

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Given: N = 500 R = 50 Ω ΔΦ_B = 0.094 Wb Formula: q = (N/R)ΔΦ_B Step 1: q = (500/50) × 0.094 C Step 2: q = 10 × 0.094 C Step 3: q = 0.94 C Answer: charge flowed = 0.94 C. Important idea: induced charge…

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For a closed circuit, I = e/R and e = -N(dΦ_B/dt). So q = IΔt = (N/R)(ΔΦ_B). The time interval cancels out. Therefore, the total charge depends only on the change in magnetic flux and the resistance.

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Given: B = 0.15 T v = 2 m/s l = 0.5 m Formula: V = Bvl Step 1: V = 0.15 × 2 × 0.5 V Step 2: V = 0.15 V Answer: motional emf = 0.15 V. Unit check: T × m/s × m = V.