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Question: A player with 3 m long iron rod runs towards east with a speed of 30 km/hr. Horizontal component of ...

A player with 3 m long iron rod runs towards east with a speed of 30 km/hr. Horizontal component of earth's magnetic field is4×10−5Wb/m24 \times 10^{- 5}Wb/m^{2}. If he is running with rod in horizontal and vertical positions, then the potential difference induced between the two ends of the rod in two cases will be

A

Zero in vertical position and 1×10−3V1 \times 10^{- 3}Vin horizontal position

B

1×10−3V1 \times 10^{- 3}Vin vertical position and zero is horizontal position

C

Zero in both cases

D

1×10−3V1 \times 10^{- 3}V in both cases

Answer

1×10−3V1 \times 10^{- 3}Vin vertical position and zero is horizontal position

Explanation

Solution

If player is running with rod in vertical position towards east, then rod cuts the magnetic field of earth perpendicularly (magnetic field of earth is south to north).

Hence Maximum emf induced is

e=Bvl=4×10−5×30×10003600×3=1×10−3volte = Bvl = 4 \times 10^{- 5} \times \frac{30 \times 1000}{3600} \times 3 = 1 \times 10^{- 3}volt

When he is running with rod in horizontal position, no field is cut by the rod, so e = 0.

e=Bvl=4×10−5×30×10003600×3=1×10−3volte = Bvl = 4 \times 10^{- 5} \times \frac{30 \times 1000}{3600} \times 3 = 1 \times 10^{- 3}volt