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Question

A jet plane is traveling towards the west at speed of 1800km/h. What is the voltage difference developed between the ends of the wing having a span of 25m, if the Earth's magnetic field at the location has a magnitude of 5×10-4T and the dip angle is 30°?


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Solution

Step 1: Given data and diagram,

Speed of jet v=1800Kmh-1

Length of wing span l=25m

Magnetic field B=5×10-4T

Dip angle δ=30°

Step 2: Formula Used

The vertical component of Earth's magnetic field is given by the formula Bv=Bsinδ.

The induced voltage can be given by the formula E=Bvvl.

Step 3: Calculate the voltage difference developed between the ends of the wing:

The velocity of the jet plane, v=1800km/h. Convert it into m/s by multiplying by 10003600.

v=1800×10003600m/sv=18000003600m/sv=500m/s

Calculate the vertical component of Earth's magnetic field (here, the vertical component is considered because only the vertical component of magnetic field is normal to both the wings and the direction of motion)

Bv=5×10-4sin30°TBv=5×10-4×12TBv=2.5×10-4T

Calculate the induced voltage

E=2.5×10-4×500×25VE=3.125V

Hence, the voltage difference developed between the ends of the wing is 3.125V.


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