#coil radius

Mutual Induction and Mutual Inductance

A circular coil of radius 8 cm and 150 turns rotates at 25 rad/s in a 0.06 T field. What is the maximum emf induced?

**Mutual inductance calculation** M = e₂/(dI₁/dt), for 200 turns length 0.5 m nearby coil e=0.5 V dI=2 A dt=0.2 s dI/dt=10 A/s, M=0.5/10=0.05 H, depends on geometry, orientation, number of turns, area, separation, coupling coefficient k = M/√(L₁ L₂) ≤1. A = π r² = 3.14 × (0.08)² = 0.0201 m² . ε₀ = N B A ω = 150 × 0.06 × 0.0201 × 25 = 4.5225 V ≈ 4.52 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

Ref: NCERT > Physics Book > Electromagnetic Induction > Mutual Induction and Mutual Inductance

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A circular coil of 80 turns and radius \( 4 \, \text{cm} \) carries a current of \( 0.5 \, \text{A} \). What is the magn

**Biot-Savart law** dB = μ₀/4π·I dl × r̂/r² underlies both straight wire and loop formulas. For square loop side a, area A = a², moment m = N I A, field pattern similar to dipole at large distances, with superposition for N turns. Magnetic field B = (μ₀ N I/2 R) . B = (4 π × 10⁻⁷ × 80 × 0.5/2 × 0.04) = (16 π × 10⁻⁶/0.08) = 2 π × 10⁻⁴ ≈ 6.28 × 10⁻⁴ T . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀ N I/(2R) and τ

Ref: NCERT > Physics Book > Moving Charge and Magnetism > Magnetic Field Due to Current - Straight Wire and Circular Loop

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A circular coil of radius \( 0.04 \, \text{m} \) with 50 turns carries \( 1.8 \, \text{A} \). What is the magnetic field

**Biot-Savart law** dB = μ₀/4π·I dl × r̂/r² underlies both straight wire and loop formulas. For square loop side a, area A = a², moment m = N I A, field pattern similar to dipole at large distances, with superposition for N turns. B = (μ₀ N I/2 R) . B = (4 π × 10⁻⁷ × 50 × 1.8/2 × 0.04) = (36 π × 10⁻⁶/0.08) = 4.5 π × 10⁻⁴ ≈ 1.41 × 10⁻³ T . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀ N I/(2R) and τ = N

Ref: NCERT > Physics Book > Moving Charge and Magnetism > Magnetic Field Due to Current - Straight Wire and Circular Loop

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A circular coil of radius \( 0.05 \, \text{m} \) with 30 turns carries \( 2.5 \, \text{A} \). What is the magnetic field

**Biot-Savart law** dB = μ₀/4π·I dl × r̂/r² underlies both straight wire and loop formulas. For square loop side a, area A = a², moment m = N I A, field pattern similar to dipole at large distances, with superposition for N turns. B = (μ₀ N I/2 R) . B = (4 π × 10⁻⁷ × 30 × 2.5/2 × 0.05) = (30 π × 10⁻⁶/0.1) = 3 π × 10⁻⁴ ≈ 9.42 × 10⁻⁴ T . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀ N I/(2R) and τ = N

Ref: NCERT > Physics Book > Moving Charge and Magnetism > Magnetic Field Due to Current - Straight Wire and Circular Loop

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A circular coil of radius \( 0.1 \, \text{m} \) with 20 turns carries \( 4 \, \text{A} \). What is the magnetic field at

**Magnetic field due to long straight wire** at distance r is B = μ₀ I/(2π r), μ₀ = 4π×10⁻⁷ T·m/A, direction circular around wire given by right-hand grip rule. For I = 18 A, r = 0.15 m, B = 2×10⁻⁷×18/0.15 = 2.4×10⁻⁵ T, illustrating 1/r dependence. B = (μ₀ N I/2 R) . B = (4 π × 10⁻⁷ × 20 × 4/2 × 0.1) = (32 π × 10⁻⁶/0.2) = 16 π × 10⁻⁵ ≈ 5.03 × 10⁻⁴ T . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀ N I/(2R)

Ref: NCERT > Physics Book > Moving Charge and Magnetism > Magnetic Field Due to Current - Straight Wire and Circular Loop

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