Question dealing with electromagnetic induction

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SUMMARY

The discussion centers on calculating the induced electromotive force (emf) in a vertical radio antenna of length 1.2 meters, as the automobile travels at 65.0 km/h through the Earth's magnetic field of 50.0 mT. The user references the motional emf equation E = -Blv, which applies when the velocity is perpendicular to the magnetic field. However, the user is confused about how to apply this equation when the angle between the velocity and the magnetic field is not 90 degrees. The key takeaway is that the angle must be considered to accurately calculate the induced emf.

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  • Understanding of electromagnetic induction principles
  • Familiarity with the motional emf equation E = -Blv
  • Knowledge of vector components in physics
  • Basic concepts of magnetic fields and their orientation
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  • Explore the implications of the angle in electromagnetic induction
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Question:
An automobile has a vertical radio antenna 1.2m long. The automobile travels at 65.0 km/h on a horizontal road where the Earth's magnetic field is 50.0 mT directed toward the north and downward at an angle of 65.0 degrees below horizontal.

calculate the magnitude of the induced emf.

I know that when a conducting bar of length l moves through a magnetic field B with a velocity of v so that v is perpendicular to B the emf is induced in the bar (called a motional emf)

E = -Blv

I'm stumped because this law only applies when the velocity and the magnetic field are perpendicular, and in this problem they are not. If anyone can explain this that would be awesome.
 
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The equation you have is a simplified one in that it assumes that they are perpendicular. So, what do we know about things that are perpendicular? This equation implies that when they are perpendicular, the voltage is at its maximum. When thinking about perpendicular and maximum, what comes to mind?
 

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