#rotating loop

A square loop of side 16 cm rotates at 18 rad/s in a 0.2 T field. What is the maximum emf induced?

**Self-inductance of solenoid** L = μ₀ N² A / l, N total turns, A cross-section, l length, for N=650 turns per meter means n=650 m⁻¹, if length 1 m N=650, A=0.014, L=4π×10⁻⁷×650²×0.014/1=0.00743 H, self-induced emf magnitude L |dI/dt|, dI/dt=12 A/s, e=0.089 V, opposes change. A = (0.16)² = 0.0256 m² . ε₀ = N B A ω = 1 × 0.2 × 0.0256 × 18 = 0.09216 V ≈ 0.092 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) and U

Ref: NCERT > Physics Book > Electromagnetic Induction > Self-Induction and Self-Inductance

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Induced EMF Due to Change in Magnetic Field

A conducting loop is rotated in a uniform magnetic field. The induced emf depends on the rate of change of what physical

**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. Faraday’s law states that the induced emf is proportional to the rate of change of magnetic flux through the loop, which varies as the loop rotates. 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 = ½ L I², result Magnetic

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

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Induced EMF Due to Change in Magnetic Field

A conducting loop is rotated in a non-uniform magnetic field. The induced emf is more complex than in a uniform field be

**Field decreasing to zero** induces emf trying to maintain field, current direction such that its field adds to original. For 150 turns area 0.06 m² B 0.14 T to zero in 0.3 s, e=150×0.06×0.14/0.3=4.2 V, as earlier, showing linear dependence on N, A, ΔB/Δt. In a non-uniform field, the magnetic field strength varies across the loop, causing the flux change rate to depend on position, leading to a non-sinusoidal emf. 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 = ½

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

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Rotational EMF and AC Generator

A square loop of side 20 cm is rotated in a 0.2 T field at 10 rad/s. What is the maximum emf induced?

**Rotational emf** when coil area A rotates with angular speed ω in uniform field B, flux Φ = B A cos ωt, emf e = -N dΦ/dt = N B A ω sin ωt, maximum e₀ = N B A ω, frequency = ω/2π. For square side 22 cm area 0.0484 m² N=1 ω=14 rad/s B=0.15 T, e₀=1×0.15×0.0484×14=0.1016 V, sinusoidal. ε₀ = N B A ω , N = 1 , A = (0.2)² = 0.04 m² . ε₀ = 1 × 0.2 × 0.04 × 10 = 0.08 V . Using Φ = B A cosθ, e = -N dΦ/dt = -N A dB/dt