A metallic rod of length l is rotated at a constant angular speed omega, normal to a uniform magnetic field B. Derive an expression for the current induced in the rod, if the resistance of the rod is R.

Consider the infinite small length dx at a distance x.


So speed of this part is x.


Induced small emf = Bx dx (since emf = vBl)


The emf between the ends of the rotating rod is


The positive charges of the rod will be pushed towards O by the magnetic field. 

Thus, the rod may be replaced by a battery of emf source with the positive terminal towards O. 


The equivalent circuit diagram is shown in figure. The circular loop joins A to C by a resistance less path. The current in the resistance R is

  • 5
What are you looking for?