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