Physics-12 : 6: Electromagnetic Induction - Flashcards

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What is responsible for the induction of current in Faraday's experiments?
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The relative motion between the magnet and the coil, or a changing magnetic field.
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# Question Answer
1 What is responsible for the induction of current in Faraday's experiments? The relative motion between the magnet and the coil, or a changing magnetic field.
2 What is magnetic flux? The flux of the magnetic field \( \mathbf{B} \) through a surface — for a plane of area \( A \) in a uniform field, \( \Phi_B = \mathbf{B}\cdot\mathbf{A} = BA\cos\theta \), where θ is the angle between \( \mathbf{B} \) and the area vector \( \mathbf{A} \).
3 What is the SI unit of magnetic flux? Weber (Wb) or T m².
4 Is magnetic flux a scalar or vector quantity? Scalar.
5 Can a strong magnet induce a current in a stationary closed loop? No. The magnetic flux must change.
6 What is the emf induced in a rotating rod of length \( R \) in a magnetic field \( B \) with angular velocity \( \omega \)? \( \varepsilon = \frac{1}{2} B \omega R^2 \).
7 What is mutual inductance? The inductance of one coil with respect to another due to the magnetic field of the second coil.
8 What is the mutual inductance of two long co-axial solenoids? \( M = \mu_0 n_1 n_2 \pi r_1^2 l \).
9 What is the self-inductance of a long solenoid? \( L = \mu_0 n^2 A l \).
10 What is the energy stored in an inductor? \( U = \frac{1}{2} LI^2 \).
11 What is the frequency of the induced emf in an AC generator? Equal to the frequency of rotation of the coil.
12 What is Faraday's law? \( \varepsilon = -N \frac{d\Phi_B}{dt} \).
13 A 1.0 m long metallic rod is rotated at 400 rad/s in a magnetic field of 0.5 T. What is the emf developed between the centre and the ring? 100 V.
14 A rectangular loop of sides 8 cm and 2 cm moves out of a magnetic field of 0.3 T at 1 cm/s. What is the induced emf when moving normal to the longer side, and how long does it last? \( \varepsilon = Bvl = 0.3\times0.01\times0.08 = 0.24 \) mV, using the longer (8 cm) side as the length \( l \) that cuts the field lines; it lasts \( 0.02/0.01 = 2 \) s, the time for the loop to cross the shorter (2 cm) dimension.
15 What is the induced emf when a circular loop is deformed into a straight wire in a magnetic field? The induced emf opposes the decrease in flux.
16 In Experiment 6.1, does it matter whether the magnet moves towards a stationary coil, or the coil moves towards a stationary magnet? No — the same deflection is observed either way, since it is the relative motion between the magnet and the coil that induces the current, not which one is actually moving.
17 When a person does work moving a bar magnet against the repulsive force exerted by the current it induces in a coil, where does that energy go? It is dissipated as Joule heating produced by the induced current in the coil.
18 What is the electrostatic analog of (self-)inductance? Capacitance — both depend on the circuit element's geometry (coil shape for \( L \); plate area and separation for \( C \)) and on an intrinsic material property (relative permeability \( \mu_r \) for \( L \); dielectric constant \( K \) for \( C \)).
19 What energy conversion does an ac generator perform? It converts mechanical energy (used to rotate the armature) into electrical energy.
20 What is the SI unit of induced emf? Volt (V).
21 Solenoids A and B are made of the same magnetic material (relative permeability \( \mu_r \)) and have equal cross-sectional area. The length of A is twice that of B, and A has half as many turns per unit length as B. What is \( L_A:L_B \)? (NEET 2024, Re-exam) 1:2 — since \( L=\mu_r\mu_0 n^2 A l \), so \( L_A/L_B = (n_A/n_B)^2\times(l_A/l_B) = (1/2)^2\times 2 = 1/2 \).
22 What is the dimensional formula of emf? \( [\text{M L}^2 \text{T}^{-3} \text{A}^{-1}] \).
23 A cycle wheel of radius 0.5 m is rotated with a speed of 10 rad/s in a region where a magnetic field of 0.1 T is perpendicular to the plane of the wheel. What is the emf generated between the centre and the rim? (NEET 2019, Odisha) 0.125 V — from \( \varepsilon = \frac{1}{2} B \omega R^2 = \frac{1}{2}\times 0.1\times 10\times 0.5^2 \), the same rotating-rod formula as Example 6.6.
24 A conducting circular loop lies in a uniform magnetic field of 0.04 T, its plane perpendicular to the field. Its radius shrinks at a constant rate of 2 mm/s. What is the induced emf when the radius is 2 cm? (AIPMT 2009) \( 1.0\times10^{-5} \) V (10 μV) — from \( \varepsilon = B\cdot 2\pi r\left|\dfrac{dr}{dt}\right| = 0.04\times2\pi\times0.02\times0.002 \).
25 If N is the number of turns in a coil (geometry otherwise fixed), how does its self-inductance L vary with N? (AIPMT 1993) \( L \propto N^2 \) — since \( L=\mu_0 n^2 Al \) with \( n=N/l \), so \( L \propto N^2/l \); for a fixed-length coil, doubling the turns quadruples L.
26 An inductor carrying a current stores its energy in what form? (AIPMT 1990 / 1989) In the magnetic field it sets up (magnetic potential energy, \( U=\frac12 LI^2 \)) — unlike a capacitor, which stores energy in its electric field.