Induced emf in a falling wire aligned with Earth's magnetic field components

[kihr]

Homework Statement

Whether a length of metallic wire, if placed in the geographic (a) east-west, and (b) north-south directions, and dropped freely from a height, would have an induced emf or not.

Homework Equations

E= - d(phi)/dt, where phi = flux intercepted by wire

The Attempt at a Solution

The magnetic field of the Earth has a vertical and a horizontal component, both of which lie on the magnetic meridian. The horizontal component (in the plane of the magnetic meridian) would further have components along the geographic N-S and E-W directions depending on the magnetic declination at the given point on the Earth's surface. Thus for (a) the falling piece of wire would cut the horizontal component of the Earth's magnetic field acting along the geographic N-S direction, and an emf would be induced. For (b) the wire would cut the horizontal component of the Earth's magnetic field acting along the geographic E-W direction, and here again an emf would be induced in the wire.

I would appreciate if the correctness of above could be confirmed. Thanks.

 

[Gib Z]

Basically what you are saying is that the magnetic north and geographic north do not align, so in either option there is some perpendicular component of the field, so there is an induced emf, which is correct.

 

[kihr]

The perpendicular component of the Earth's magnetic field is not intercepted by the wire irrespective of whether it is aligned along the geographic N-S or E-W direction. However, the component of the Earth's horizontal magnetic field (i.e. in the plane of the magnetic meridian) along the geographic N-S and E-W directions do get intercepted by the falling wire aligned along the E-W and N-S directions respectively. This gives rise to the induced emf. I hope I have been able to make my point of view clear. Thanks.