Electromagnetic induction
Electromagnetic induction
- A conducting rod of length 1 m moves at 5 m/s perpendicular to a uniform magnetic field of 0.4 T on frictionless rails connected through a 4 Ω resistor (other resistances negligible). The external force needed to keep it moving at constant speed is Answer: D. 0.2 N e=Blv=2 V, I=0.5 A, F=BIl=0.4×0.5×1=0.2 N. 1
- When the current in a coil falls uniformly from 2 A to zero in 0.05 s, an emf of 8 V is induced in it. The self-inductance of the coil is Answer: A. 0.2 H L=e/dI/dt=8/2/0.05=0.2 H. 1
- A toroidal ring, having 100 turns per cm of a thin wire is wound on a nonmagnetic metal rod of length 1 m and diameter Data : l = 1 m, d = 1 cm, n = 100 cm⁻¹ = 10⁴ m⁻¹, I = 100 A, µ₀ = 4π × 10⁻⁷ H/m The radius of cross section, r = d/2 = 0.5 cm = 5 × 10⁻³ m (... 2
- The primary and secondary coil of a transformer each have an inductance of 200 × 10-6H. Data: L_P = L_S = 2 × 10⁻⁴ H, M = 4 × 10⁻⁶ H M = K sqrtL_P L_S The coupling coefficient is K = fracMsqrtL_P L_S=frac4 × 10⁻⁶sqrt(2 × 10⁻⁴)²=... 1
- A long solenoid of length l, cross-sectional area A and having N1 turns (primary coil) has a small coil of N2 We assume the solenoid to be ideal and that all the flux from the solenoid passes through the outer coil C. For a steady current Is through... 1
- An emf of 96.0 mV is induced in the windings of a coil when the current in a nearby coil is increasing Data: |e₂| = 9.6 × 10⁻² V, dI₁/dt = 1.2 A/s |e₂| = M fracd I₁d t Mutual inductance, M = frac|e₂|d I₁ / d t=frac9.6 × 10⁻²1.2 = 8 × 10⁻² H =... 1
- The value of mutual inductance of two coils is 10 mH. If the current in one of the coil changes Data: M = 10 mH = 10⁻² H, I₁i = 5A, I₁f = 1 A, ∆t = 0.2s The mutually induced emf in coil 2 due to the changing current in coil 1, e₂₁ = -M... 1
- Calculate the value of induced emf between the ends of an axle of a railway carriage 1.75 m long traveling Data: l = 1.75 m, v = 50 km/h = 50 × 5/18 m/s. B_v = 5 × 10⁻⁵ T The area swept out by the wing per unit time = 1v. ∴ The magnetic flux cut b... 1
- A stiff semi-circular wire of radius R is rotated in a uniform magnetic field B about an axis passing through its ends. Answer: Amplitude of the emf e₀ = π²R²Bf (taking B perpendicular to the axis of rotation). The semicircular wire, together with the line joi... 1
- A search coil having 2000 turns with area 1.5 cm2 is placed in a magnetic field of 0.60T. The coil is moved Data: N = 2000, A_i = 1.5 × 10⁻⁴ m², A_f = 0, B = 0.6T, ∆t = 0.2s Initial flux, NΦ_f = NBA_i = 2000(0.6)(1.5 × 10⁻⁴) = 0.18 Wb Final flux, N... 1
- In a Faraday disc dynamo, a metal disc of radius R rotates with an angular velocity ω about an axis perpendicular Suppose a thin conducting disc of radius R is rotated anticlockwise, about its axis, in a plane perpendicular to a uniform magnetic field of... 1
- State and explain Lenz’s law in the light of principle of conservation of energy. Lenz’s law : The direction of the induced current is such as to oppose the change that produces it. The change that induces a current may be... 2
- What do you mean by electromagnetic induction? State Faraday’s law of induction. The phenomenon of production of emf in a conductor or circuit by a changing magnetic flux through the circuit is called electromagnetic indu... 1