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  4. A helicopter rises vertically with a speed of 100 ms -1. If helicopter has length 10 m and horizontal component of earth's magnetic field is 5 × 10-3 Wbm -2, then the induced emf between the tip of nose and tail of helicopter is

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Q. A helicopter rises vertically with a speed of $100\, ms ^{-1}$. If helicopter has length $10\, m$ and horizontal component of earth's magnetic field is $5 \times 10^{-3} \, Wbm ^{-2}$, then the induced emf between the tip of nose and tail of helicopter is

Electromagnetic Induction

Solution:

In case of motional emf, the motion of the conductor in the field exerts force on the free charge in conductor, so that one end of the conductor becomes positive, while the other negative resulting in a potential difference across its ends due to which a non-conservative electric field is set up in the conductor. In steady state the magnetic force on the free charge is balanced by the electric force due to induced field.
$q E =q v B $
$\Rightarrow q(V / l)=q v B $
i.e., $ V =B v l$
So, the induced emf between tip of nose and tail of helicopter is given by
$\varepsilon=B v l=5 \times 10^{-3} \times 10 \times 100=5\, V$