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#decreasing field

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A flat coil is placed in a magnetic field that decreases with time. The direction of the induced current is such that it

**Induced emf due to B change** e = -N A dB/dt, N turns, A area (m²), dB/dt rate of change of field (T/s). For 110 turns area 0.035 m² B 0.09 T to 0 in 0.5 s, dB/dt=0.18 T/s, e=110×0.035×0.18=0.693 V, direction opposes decrease via Lenz's law. Lenz’s law dictates that the induced current opposes the decrease in flux by producing a magnetic field in the same direction as the original field. Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L = μ₀ N²A/l, M = e/(dI/dt) and U

Ref: NCERT > Physics Book > Electromagnetic Induction > Induced EMF Due to Change in Magnetic Field

A coil of 110 turns and area 0.035 m² is in a field that decreases from 0.09 T to 0 in 0.5 s. What is the induced emf?

**Uniform field change** in coil produces emf proportional to area and turns, for circular coil radius 0.16 m area πr²=0.0804 m², B 0.12 T deformed to wire in 0.6 s, ΔΦ=0.12×0.0804=0.00965 Wb, e=0.00965/0.6=0.0161 V, illustrating area change also induces emf. Δ Φ = B A = 0.09 × 0.035 = 0.00315 Wb . ε = N (Δ Φ/Δ t) = 110 × (0.00315/0.5) = 110 × 0.0063 = 0.693 V ≈ 0.69 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt = B l v = N B A ω sinωt, L = μ₀ N²A/l, M = e/(dI/dt)

Ref: NCERT > Physics Book > Electromagnetic Induction > Induced EMF Due to Change in Magnetic Field