An automobile has a vertical antenna 1.45 m long. The automobile travels at 90 km/h on a horizontal road where the Earth's magnetic field is 59.0 µT directed to the north and downward at an angle of 65.5° below the horizontal. Calculate the maximum magnitude of the induced emf in the antenna.

Respuesta :

Answer:

[tex]9.05\times 10^{-4} V[/tex]

Explanation:

We are given that

Length of antenna,l=1.45 m

Earth's magnetic field,[tex]B=59\mu T=59\times 10^{-6} T[/tex]

[tex]1\mu=10^{-6}[/tex]

[tex]\theta=65.5^{\circ}[/tex]

Speed,v=90 km/h=[tex]90\times \frac{5}{18}=25m/s[/tex]

[tex]1km/h=\frac{5}{18}m/s[/tex]

Magnitude of maximum induced emf in the antenna=[tex]E=Blvcos\theta[/tex]

Substitute the values

[tex]E=59\times 10^{-6}\times 1.45\times 25cos65[/tex]

[tex]E=9.05\times 10^{-4} V[/tex]