physics help needed please..

Question

A boat is moving due east where the earths magnetic field is 5.0 X (10 ^-5 ) N/Am due north and horizontal .
The boat carries a vertical aerial 2 metres long. if the speed of the boat is 1.5 m/s. The magnitude of emf induced in the aerial wire is ?

1. 0.75 mV
2. 0.50 mV
3. 0.15 mV
4. 1.0 mV

Answer 1

Probably waaaay too late to do anyone any good, but this is a case of motional EMF.

 

When a conductor is moved through a magnetic field, the free charges in the conductor get pushed around, and positive and negative charges end up piling up at opposite ends.  This sets up a potential difference across the length of the conductor.  Since the velocity is perpendicular to the magnetic field here, the formula for that EMF (voltage) is:

 

emf = Blv

 

where

 

B = (uniform) magnetic field magnitude

l = length of conductor

v = speed of conductor moving through the field

 

In this case,  emf = (5 x 10^-5 T)(2 m)(1.5 m/s) = 1.5 x 10^-4 V = 0.15 mV... so number 3 is correct.