A circular coil of radius $8\,\mathrm{cm}$ and $20$ turns rotates about its vertical diameter with an angular speed of $50\,\mathrm{s}^{-1}$ in a uniform horizontal magnetic field of magnitude $3 \times 10^{-2}\,\mathrm{T}$. Find the maximum and average value of the emf induced in the coil.

$\varepsilon_{\max} \approx 0.603\,\mathrm{V}$; average emf over a full cycle $= 0$.

CBSE Class 12 · 2005 · All India · Electromagnetic InductionShort Answer

A circular coil of radius

8 cm

and

20

turns rotates about its vertical diameter with an angular speed of

50 s^{- 1}

in a uniform horizontal magnetic field of magnitude

3 \times 1 0^{- 2} T

. Find the maximum and average value of the emf induced in the coil.

Answer: $ε_{m a x} \approx 0.603 V$ ; average emf over a full cycle $= 0$ .

Solution

For a coil rotating in a uniform field the peak emf is

ε_{m a x} = N B A ω

.
Area:

A = π r^{2} = π (8 \times 1 0^{- 2})^{2} = 64 π \times 1 0^{- 4} m^{2}

ε_{m a x} = N B A ω = 20 \times (3 \times 1 0^{- 2}) \times (64 π \times 1 0^{- 4}) \times 50

ε_{m a x} \approx 0.603 V

Over a complete cycle the emf is sinusoidal, so its average value is

ε_{avg} = 0

CBSE Class 12 Board · 2005 · All India · Subjective

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