Question

An automobile has a vertical radio antenna 1.10 m long. The automobile travels at70.0 km/h on a horizontal road wherethe Earth's magnetic field is 50.0 µT, directed toward thenorth and downwards at an angle of 65.0° below thehorizontal.

(a) Specify the direction the automobile should move in order togenerate the maximum motional emf in the antenna, with the top ofthe antenna positive relative to the bottom.

Answer 1

a) East direction and magnitude
`E_(mf)=4.509x10^(-4) V`

Step-by-step explanation:

The magnetic field is in the north direction and have 65 angle so to form a 90 angle the east direction for the generate the maximum motional Emf

check:

`E_(mf)=\beta*l*v`

`v=70(km)/(h)*(1000m)/(1km)*(1h)/(3600s)=19.4(m)/(s)`

`E_(mf)=\beta*cos(65)*l*v`

now taking just the magnetic field to determinate the maximum Emf

`E_(mf)=50uT*cos(65)*1.1m*19.4(m)/(s)`

`E_(mf)=50x10^(-6)T*0.4226*1.10m*19.4(m)/(s)`

`E_(mf)=4.509x10^(-4) V`