Question

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.

Answer 1

Answer:

$9.05\times 10^{-4} V$

Explanation:

We are given that

Length of antenna,l=1.45 m

Earth's magnetic field,$B=59\mu T=59\times 10^{-6} T$

$1\mu=10^{-6}$

$\theta=65.5^{\circ}$

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

$1km/h=\frac{5}{18}m/s$

Magnitude of maximum induced emf in the antenna=$E=Blvcos\theta$

Substitute the values

$E=59\times 10^{-6}\times 1.45\times 25cos65$

$E=9.05\times 10^{-4} V$