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

A) 50 V
B) 0.5 V
C) 5 V
D) 25 V
Explanation

(c) In case of motional emf, the motion of the conductor in the field exerts a force on the free charge in the 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.
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ qE = qvB$
or $\ \ \ \ \ \ \ \ \ \ \ \ q\left( \frac{V}{l} \right) = qvB$
$ie,$ $V = Bvl$
So, the induced emf between tip of nose and tail of helicopter is given by
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ e = Bvl$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 5 \times 10^{- 3} \times 10 \times 100 = 5V$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.