Magnetic Field Due to Current - Straight Wire and Circular Loop

Magnetic Field Due to Current - Straight Wire and Circular Loop

A square loop of side \( 0.25 \, \text{m} \) with 20 turns carries \( 2.5 \, \text{A} \) in a magnetic field of \( 0.3 \

**Field at centre of circular loop** with N turns is B = μ₀ N I/(2R), R radius (m), direction along axis via right-hand rule, magnitude proportional to N I/R. For R = 0.09 m, N = 45, I = 1.2 A, B = 4π×10⁻⁷×45×1.2/(2×0.09) = 3.77×10⁻⁴ T, showing N enhancement. Torque tau = N I A B sin θ , where A = 0.25 × 0.25 = 0.0625 m² . tau = 20 × 2.5 × 0.0625 × 0.3 × sin 45° = 0.9375 × 0.707 = 0.6633 ≈ 0.66 N m . Using F = q v B sinθ, F = I l B

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A square loop of side \( 0.12 \, \text{m} \) with 35 turns carries \( 1.8 \, \text{A} \) in a magnetic field of \( 0.5 \

**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. Torque tau = N I A B sin θ , where A = 0.12 × 0.12 = 0.0144 m² . tau = 35 × 1.8 × 0.0144 × 0.5 × sin 30° = 0.9072 × 0.5 = 0.4536 ≈ 0.45 N m . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A circular coil of radius \( 0.11 \, \text{m} \) with 25 turns carries \( 3 \, \text{A} \). What is the magnetic field a

**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 × 25 × 3/2 × 0.11) = (30 π × 10⁻⁶/0.22) = 1.3636 π × 10⁻⁴ ≈ 4.28 × 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 = N

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A circular loop of radius \( 0.2 \, \text{m} \) with 10 turns carries \( 1.5 \, \text{A} \). What is the magnetic field

**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. Magnetic field B = (μ₀ N I/2 R) . B = (4 π × 10⁻⁷ × 10 × 1.5/2 × 0.2) = (6 π × 10⁻⁶/0.4) = 1.5 π × 10⁻⁵ ≈ 4.71 × 10⁻⁵ T . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A long straight wire carries a current of \( 25 \, \text{A} \). What is the magnetic field at a distance of \( 0.25 \, \

**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 I/2 π r) . B = (4 π × 10⁻⁷ × 25/2 π × 0.25) = (100 × 10⁻⁷/0.5) = 2 × 10⁻⁵ 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 I A B sinθ, result

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A square loop of side \( 0.16 \, \text{m} \) with 25 turns carries \( 3 \, \text{A} \) in a magnetic field of \( 0.7 \,

**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. Torque tau = N I A B sin θ , where A = 0.16 × 0.16 = 0.0256 m² . tau = 25 × 3 × 0.0256 × 0.7 × sin 45° = 1.344 × 0.707 = 0.9502 ≈ 0.95 N m . Using F = q v B sinθ, F = I l B sinθ, B =

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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

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A long straight wire carries a current of \( 30 \, \text{A} \). What is the magnetic field at a distance of \( 0.3 \, \t

**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. Magnetic field B = (μ₀ I/2 π r) . B = (4 π × 10⁻⁷ × 30/2 π × 0.3) = (120 × 10⁻⁷/0.6) = 2 × 10⁻⁵ 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 I

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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

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A long straight wire carries a current of \( 22 \, \text{A} \). What is the magnetic field at a distance of \( 0.2 \, \t

**Field at centre of circular loop** with N turns is B = μ₀ N I/(2R), R radius (m), direction along axis via right-hand rule, magnitude proportional to N I/R. For R = 0.09 m, N = 45, I = 1.2 A, B = 4π×10⁻⁷×45×1.2/(2×0.09) = 3.77×10⁻⁴ T, showing N enhancement. Magnetic field B = (μ₀ I/2 π r) . B = (4 π × 10⁻⁷ × 22/2 π × 0.2) = (88 × 10⁻⁷/0.4) = 2.2 × 10⁻⁵ T . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀ N I/(2R) and τ

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A rectangular loop of area \( 0.05 \, \text{m}^2 \) with 15 turns carries \( 2 \, \text{A} \) in a field of \( 1 \, \tex

**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. tau = N I A B sin θ , θ = 90° to plane means sin 0° = 1 with normal. tau = 15 × 2 × 0.05 × 1 × 1 = 1.5 N m . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀ N I/(2R) and τ

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A circular loop of radius \( 0.14 \, \text{m} \) with 15 turns carries a current of \( 4 \, \text{A} \). What is the mag

**Field at centre of circular loop** with N turns is B = μ₀ N I/(2R), R radius (m), direction along axis via right-hand rule, magnitude proportional to N I/R. For R = 0.09 m, N = 45, I = 1.2 A, B = 4π×10⁻⁷×45×1.2/(2×0.09) = 3.77×10⁻⁴ T, showing N enhancement. Magnetic field B = (μ₀ N I/2 R) . B = (4 π × 10⁻⁷ × 15 × 4/2 × 0.14) = (24 π × 10⁻⁶/0.28) = (6 π/7) × 10⁻⁵ ≈ 2.69 × 10⁻⁴ T . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r),

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