(a) Draw a labelled diagram of an ac generator. Obtain the expression for the emf induced in the rotating coil of N turns each of cross-sectional area A, in the presence of a magnetic field B.

(b) A horizontal conducting rod 10 m long extending from east to west is falling with a speed 5·0 ms^–1 at right angles to the horizontal component of the Earth’s magnetic field, 0·3×10^–4 Wb m^–2. Find the instantaneous value of the emf induced in the rod.

Question

(a) Draw a labelled diagram of an ac generator. Obtain the expression for the emf induced in the rotating coil of N turns each of cross-sectional area A, in the presence of a magnetic field B.

(b) A horizontal conducting rod 10 m long extending from east to west is falling with a speed 5·0 ms^–1 at right angles to the horizontal component of the Earth’s magnetic field, 0·3×10^–4 Wb m^–2. Find the instantaneous value of the emf induced in the rod.

Infinity Learn · Accepted Answer

(a) Labelled diagram of an ac generator.
Question Image
Expression for the emf induced in the rotating coil of N turns each of cross-sectional area A, in the presence of a magnetic field B.
In coil A, the area of coil and B the magnetic induction, then flux ϕ linked with the coil is given by
ϕ = B.A
ϕ = B.A cos ωt
The e.m.f induced in the coil is given by
$\begin{array}{l} e = - N \frac{dϕ}{dt} \\ e = - N \frac{d}{dt} (BAcos ωt) \\ e = + NBAωsin ωt \\ e = eosin ωt \end{array}$

OR
$(b) e = B_{H} lv \begin{array}{l} = 0 .3 \times 10^{- 4} \times 10 \times 5 \\ e = 15 \times 10^{- 4} V \end{array}$

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