A jet plane having a wing - span of 25 m is travelling horizontally towards east with a speed of 3600 km /hour . If the the Earth's magnetic field at the location is `4xx10^(-4)` T and the angle of dip is `30^@` , then the potential difference between the ends of the wing is

Options

A. 4 V
B. 5 V
C. 2 V
D. 2.5 V

Answer

B

Explanation

Here,
Wing - span, l = 25 m
Speed of the place , `v = 3600 "km h"^(-1)`
`=3600xx5/18"m s"^(-1)=1000 " m s"^(-1)`
Earth's magnetic field , `B = 4 xx10^(-4)T`
Angle of dip , `delta=30^@`
As the place moving horizontally toward east, it will cut the vertical component of the Earth's magnetic field which is given by
`B_V=Bsindelta=(4xx10^(-4)T)sin30^@`
`=(4xx10^(-4)T)1/2=2xx10^(-4)T`
The potential difference (i.e, induced emf) developed between the ends of the wing is
`epsilon=B_Vlv=(2xx10^(-4))(25m)(100 ms^(-1))=5V`