(a) State Lenz's law. In a closed circuit, the induced current opposes the change in magnetic flux that produced it, in accordance with the law of conservation of energy. Justify this. (b) A metal rod of length $2\,\mathrm{m}$ is rotated with a frequency of $60\,\mathrm{rev/s}$ about an axis passing through its centre and perpendicular to its length. A uniform magnetic field of $2\,\mathrm{T}$ perpendicular to its plane of rotation is switched on in the region. Calculate the emf induced between the centre and one end of the rod.

(a) See justification. (b) $\varepsilon = 120\pi\,\mathrm{V} \approx 377\,\mathrm{V}$.

CBSE Class 12 · 2024 · Electromagnetic InductionShort Answer

(a) State Lenz's law. In a closed circuit, the induced current opposes the change in magnetic flux that produced it, in accordance with the law of conservation of energy. Justify this.
(b) A metal rod of length

2 m

is rotated with a frequency of

60 rev/s

about an axis passing through its centre and perpendicular to its length. A uniform magnetic field of

2 T

perpendicular to its plane of rotation is switched on in the region. Calculate the emf induced between the centre and one end of the rod.

Answer: (a) See justification.
(b) $ε = 120 π V \approx 377 V$ .

Solution

(a) Lenz's law: the induced current flows so as to oppose the change in flux that causes it. The opposition forces the agent producing the change to do work; this work reappears as the electrical energy of the induced current. If the current aided the change, energy would be produced without any work being done, violating conservation of energy. Hence the opposition demanded by Lenz's law is required by energy conservation.
(b) Each half of the rod is a rod of length

r = L /2 = 1 m

rotating about one end; the emf between the centre and an end is

ε = \frac{1}{2} B ω r^{2}, ω = 2 π f = 2 π (60) = 120 π rad s^{- 1}

ε = \frac{1}{2} (2) (120 π) (1)^{2}

ε = 120 π V \approx 377 V

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CBSE Class 12 · 2024 · Electromagnetic InductionShort Answer

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