#torque

Torque on Current Loop, Magnetic Moment and Galvanometer

A square loop of side \( 0.15 \, \text{m} \) with 50 turns carries \( 1 \, \text{A} \) in a magnetic field of \( 0.6 \,

**Torque on current loop** in magnetic field B is τ = N I A × B, magnitude τ = N I A B sinθ, N turns, I current (A), A area (m²) = l×b for rectangular, θ angle between normal to plane and B. Maximum when plane parallel to B (θ=90°), zero when perpendicular (θ=0°), magnetic moment m = N I A direction along normal via right-hand rule. Torque tau = N I A B sin θ , where A = 0.15 × 0.15 = 0.0225 m² . tau = 50 × 1 × 0.0225 × 0.6 × sin 30° = 0.675 × 0.5 =

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Torque on Current Loop, Magnetic Moment and Galvanometer

A rectangular loop of area \( 0.06 \, \text{m}^2 \) with 15 turns carries \( 2.5 \, \text{A} \) in a field of \( 0.8 \,

**Magnetic moment of loop** m = N I A (A·m²), potential energy U = -m·B = -N I A B cosθ, torque tends to align m with B. For square side 0.18 m, A = 0.0324 m², N=30, I=2 A, B=0.4 T, θ=60°, τ =30×2×0.0324×0.4×sin60° =0.7776×0.866=0.673 N·m, illustrating large torque for modest parameters. tau = N I A B sin θ , where θ = 60° to plane means sin 30° with normal. tau = 15 × 2.5 × 0.06 × 0.8 × sin 60° = 1.8 × 0.866 = 1.5588 ≈ 1.56 N m . Using F = q v B sinθ, F =

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Solenoid, Toroid and Ampere's Law

What happens to the torque on a rectangular current loop if the magnetic field direction is reversed?

**Solenoid field** inside long solenoid is B = μ₀ n I, n = N/L turns per meter (m⁻¹), uniform and parallel to axis, outside negligible for long solenoid because fields from opposite sides cancel. For n = 1200 m⁻¹, I = 1 A, B = 4π×10⁻⁷×1200 = 1.51×10⁻³ T = 1.51 mT. Torque is given by boldsymboltau = m × B . Reversing the magnetic field B reverses the direction of the torque vector, but its magnitude remains the same. 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 > Solenoid, Toroid and Ampere's Law

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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 Force on Moving Charge - Lorentz Force and Motion

A rectangular loop of area \( 0.03 \, \text{m}^2 \) with 20 turns carries \( 4 \, \text{A} \) in a field of \( 0.9 \, \t

**Effect of doubling velocity** on magnetic force F = q v B sinθ is linear increase, F doubles for same θ and B. Electron with charge 1.6×10⁻¹⁹ C, v = 4.5×10⁶ m/s, B = 0.35 T, θ = 90°, F = 1.6×10⁻¹⁹×4.5×10⁶×0.35 = 2.52×10⁻¹³ N, illustrating magnitude for typical lab values. tau = N I A B sin θ , θ = 90° to plane means sin 0° = 1 with normal. tau = 20 × 4 × 0.03 × 0.9 × 1 = 2.16 N m . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π

Ref: NCERT > Physics Book > Moving Charge and Magnetism > Magnetic Force on Moving Charge - Lorentz Force and Motion

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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 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 rectangular loop of area \( 0.08 \, \text{m}^2 \) with 15 turns carries \( 2.5 \, \text{A} \) in a field of \( 0.6 \,

**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 , where θ = 30° to plane means sin 60° with normal. tau = 15 × 2.5 × 0.08 × 0.6 × sin 30° = 1.8 × 0.5 = 0.9 N m . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π r), B = μ₀

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 square loop of side \( 0.2 \, \text{m} \) with 30 turns carries \( 1.5 \, \text{A} \) in a magnetic field of \( 0.4 \,

**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 = 0.2 × 0.2 = 0.04 m² . tau = 30 × 1.5 × 0.04 × 0.4 × sin 60° = 1.8 × 0.4 × 0.866 = 0.6235 ≈ 0.62 N m . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π

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

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Magnetic Force on Moving Charge - Lorentz Force and Motion

A rectangular loop of area \( 0.08 \, \text{m}^2 \) with 10 turns carries \( 4 \, \text{A} \) in a field of \( 0.9 \, \t

**Effect of doubling velocity** on magnetic force F = q v B sinθ is linear increase, F doubles for same θ and B. Electron with charge 1.6×10⁻¹⁹ C, v = 4.5×10⁶ m/s, B = 0.35 T, θ = 90°, F = 1.6×10⁻¹⁹×4.5×10⁶×0.35 = 2.52×10⁻¹³ N, illustrating magnitude for typical lab values. tau = N I A B sin θ , θ = 90° to plane means sin 0° = 1 with normal. tau = 10 × 4 × 0.08 × 0.9 × 1 = 2.88 N m . Using F = q v B sinθ, F = I l B sinθ, B = μ₀ I/(2π

Ref: NCERT > Physics Book > Moving Charge and Magnetism > Magnetic Force on Moving Charge - Lorentz Force and Motion

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Magnetic Field Due to Current - Straight Wire and Circular Loop

A square loop of side \( 0.1 \, \text{m} \) with 25 turns carries \( 2 \, \text{A} \) in a magnetic field of \( 0.8 \, \

**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 = 0.1 × 0.1 = 0.01 m² . tau = 25 × 2 × 0.01 × 0.8 × sin 30° = 0.5 × 0.8 × 0.5 = 0.2 N m . Using F = q v B sinθ, F = I l B sinθ, B =

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 square loop of side \( 0.18 \, \text{m} \) with 30 turns carries \( 2 \, \text{A} \) in a magnetic field of \( 0.4 \,

**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 = 0.18 × 0.18 = 0.0324 m² . tau = 30 × 2 × 0.0324 × 0.4 × sin 60° = 0.7776 × 0.866 = 0.6734 ≈ 0.67 N m . Using F = q v B sinθ, F = I l B

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

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