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#area change

3 public questions tagged with this topic.

AC Generator, Back EMF and Time Duration of EMF

A circular loop of radius 13 cm is deformed into a straight wire in a 0.18 T field in 0.6 s. What is the induced emf?

**Back emf** in motor opposes applied voltage, e_b = N B A ω sin ωt, reduces net current, at start ω=0 e_b=0 current large, as speed increases e_b increases limiting current, power conversion mechanical, principle of motor and generator reciprocity. Initial flux: Φ = B A = 0.18 × π × (0.13)² = 0.00956 Wb . Final flux = 0. ε = (Δ Φ/Δ t) = (0.00956/0.6) = 0.01593 V ≈ 0.016 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 > AC Generator, Back EMF and Time Duration of EMF

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Self-Induction and Self-Inductance

A conducting loop is twisted in a uniform magnetic field. The induced emf arises primarily from what change?

**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. Twisting changes the orientation of the loop’s area vector relative to the field, altering the magnetic flux and inducing an 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 L I², result Change in

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

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Latent Heat and Phase Transitions

A copper plate has an area of 0.8m2 at 60∘C. What is the decrease in area when cooled to 10∘C? (αl\=1.7×10−5K−1)

Given: A0 = 0.8m2, ΔT = 10−60 = −50∘C, αl = 1.7×10−5K−1. ΔA = A0×2αlΔT = 0.8×2×1.7×10−5×(−50). ΔA = 0.8×3.4×10−5×(−50) = −0.00136m2 (decrease of 0.00136m2). As per NCERT, applying relevant law/formula with correct units and sign convention leads to 0.00136 m². This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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