A metallic rod of length l is rotated at a constant angular speed omega, normal to a uniform magnetic field - Physics - Electromagnetic Induction

Question

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

Roopa jayasimha · Accepted Answer

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

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.