CAN U PLZ ANSWER THIS: A metallic rod of length l is rotated at a constant angular speed , - Physics -

Question

CAN U PLZ ANSWER THIS: A metallic rod of length
l is rotated at a constant angular
speed ω , 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

Vijay Yadav · Accepted Answer

Consider the infinitesimly small length dx at a distance x.

So speed of this part is ωx.

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

The emf between the ends of the rotating rod is

$ϵ = \int d ϵ = {\int B}_{0}^{l} ω x d x = \frac{1}{2} B ω l^{2}$

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 $\frac{1}{2} B ω l^{2}$ 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

$i = \frac{ϵ}{R} = \frac{B ω l^{2}}{2 R}$

CAN U PLZ ANSWER THIS: A metallic rod of length l is rotated at a constant angular speed ω , 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 .