A wheel with 8 metallic spokes, each $50\,\mathrm{cm}$ long, is rotated with a speed of $120\,\mathrm{rev/min}$ in a plane normal to the horizontal component of the Earth's magnetic field. The Earth's magnetic field at the place is $0.4\,\mathrm{G}$ and the angle of dip is $60^{\circ}$. Calculate the emf induced between the axle and the rim of the wheel. How will the value of the emf be affected if the number of spokes is increased?

$\varepsilon \approx 3.14 \times 10^{-5}\,\mathrm{V}$; the emf is unaffected by the number of spokes.

CBSE Class 12 · 2013 · Delhi · Electromagnetic InductionShort Answer

A wheel with 8 metallic spokes, each

50 cm

long, is rotated with a speed of

120 rev/min

in a plane normal to the horizontal component of the Earth's magnetic field. The Earth's magnetic field at the place is

0.4 G

and the angle of dip is

6 0^{\circ}

. Calculate the emf induced between the axle and the rim of the wheel. How will the value of the emf be affected if the number of spokes is increased?

Answer: $ε \approx 3.14 \times 1 0^{- 5} V$ ; the emf is unaffected by the number of spokes.

Solution

Only the horizontal component of the Earth's field is normal to the plane of rotation:

B_{H} = B cos δ = (0.4 \times 1 0^{- 4}) cos 6 0^{\circ} = 2 \times 1 0^{- 5} T

Angular speed:

ω = 2 π (\frac{120}{60}) = 4 π rad s^{- 1}

.
Each spoke is a rod rotating about one end, so the emf between axle and rim is

ε = \frac{1}{2} B_{H} ω R^{2} = \frac{1}{2} (2 \times 1 0^{- 5}) (4 π) (0.5)^{2}

ε \approx 3.14 \times 1 0^{- 5} V

All spokes are in parallel between the same two points (axle and rim), so they share the same emf; increasing the number of spokes does not change the induced emf.

CBSE Class 12 Board · 2013 · Delhi · Subjective

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CBSE Class 12 · 2013 · Delhi · Electromagnetic InductionShort Answer

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