Question dealing with electromagnetic induction

[DSUND34]

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.

 

[PaintballerCA]

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?

 

[Moetasim]

I can explain that the formula E = -Blv is a simplified version of Faraday's law of electromagnetic induction. This law states that the induced electromotive force (EMF) is equal to the rate of change of magnetic flux through a circuit. In this case, the vertical radio antenna can be considered as a circuit, and the magnetic flux through it is changing as the automobile moves through the Earth's magnetic field.

To calculate the magnitude of the induced EMF, we need to consider the angle between the velocity and the magnetic field. This can be done by using the component of the velocity that is perpendicular to the magnetic field, which in this case is v*sin(65°). So the formula for the magnitude of the induced EMF would be:

E = -B * l * v * sin(65°)

Substituting the given values, we get:

E = (-0.05 T) * (1.2 m) * (65 km/h * 1000 m/km * 1h/3600s) * sin(65°)

E = -1.25 V

Therefore, the magnitude of the induced EMF in this scenario is approximately 1.25 V. It is important to note that the negative sign indicates that the induced EMF is in the opposite direction to the motion of the automobile. I hope this explanation helps to clarify the concept of electromagnetic induction in this scenario.