Question

An automobile has a vertical radio antenna 1.45 m long. The automobile travels at 70.0 km/h on a horizontal road where Earth's magnetic field is 50.0 µT, directed toward the north and downward at an angle of 65.0° below the horizontal. (a) Specify the direction the automobile should move so as to generate the maximum motional emf in the antenna, with the top of the antenna positive relative to the bottom. north east west south (b) Calculate the magnitude of this induced emf. mV

Answer 1

Answer:

595.73 X 10⁻⁶ V.

Explanation:

The magnetic field is towards the north with dip angle equal to 65 so the horizontal component of earth's magnetic field will be

H = 50 X 10⁻⁶ Cos 65 = 21.13 x 10⁻⁶ T.

length of rod L = 1.45 M

Velocity of rod = 70 km / h = 19.444 m /s

Since the top of the antenna rod is to have positive polarity , current induced in it will be from down to up . Magnetic field is towards the north .

To cut magnetic flux perpendicularly , rod should move towards the east .

We can easily get this direction by applying Fleming's right  hand Rule.

Induced emf =  H L v

= 21.13 x 10⁻⁶ X 1.45 X 19.444

= 595.73 X 10⁻⁶ V.