# Homework Help: Magnitude of induced e.m.f

1. Oct 7, 2006

### Amith2006

1)A car moves on a plane road. The induced e.m.f in the axle connecting the 2 wheels is maximum when it moves:
a)eastward at the equator
b)westward at the equator
c)eastward in the latitude 45 degrees
d)at the poles
I analyzed in the following way:
The induced e.m.f depends on both magnetic field & the angle (theta) between the direction of motion and magnetic field vector. The magnitude of the earth’s total magnetic field at the equator is equal to earth’s total magnetic field at the poles. So, as the magnetic field is the same, the magnitude of induced e.m.f depends only on theta. When moving along the equator, eastward or westward, theta is 90 degrees because the magnetic field points from south to north and along the earth’s surface. So, in this case the induced e.m.f is maximum. When moving along the poles, theta is 90 degrees because at the poles the earth’s magnetic field is entirely vertical and perpendicular to earth's surface. So in this case also the induced e.m.f is maximum. So, options (a),(b) and (c) seems to be right. But the answer given in my book is option (d). Please help.

2. Oct 7, 2006

### Astronuc

Staff Emeritus
The induction of EMF depends on the angle of the magnetic fields lines with the axis (orientation) of the conductor, in addition to the magnitude (field intensity). This is a manifestation of the Lorentz force.

http://hyperphysics.phy-astr.gsu.edu/Hbase/magnetic/genwir.html

At the equator the magnetic field lines are more or less parallel with the surface of the earth. At latitude 45°, the field lines are nearly perpendicular to the surface, but the intensity is not as great as that at poles. At the poles, the field line density is maximum and the angle is steepest, essentially perpendicular. See these examples - http://hyperphysics.phy-astr.gsu.edu/Hbase/magnetic/magfie.html#c1

or http://hyperphysics.phy-astr.gsu.edu/Hbase/magnetic/magearth.html

For maximum EMF, the cars axle must be perpendicular to the applied magnetic field and the intensity of the magnetic field must be maximum.