Motional EMF in rotating rod Class 12

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In this article, we will derive an expression for induced emf in a rod rotating in a uniform magnetic field. So let’s get started…

Motional EMF in rotating rod Class 12

Motional EMF in rotating rod Class 12
Rod rotating in a uniform magnetic field

Consider a metallic rod OA of length l, which is rotating with angular velocity ω in a uniform magnetic field B, the plane of rotation is perpendicular to the magnetic field.

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A rod may be supposed to be formed of a large number of small elements. Consider a small element of length dx at a distance X from the center. If v is the linear velocity of this element, then the area swept by the element per second is vdx. According to Faraday’s law of electromagnetic induction. EMF induced in the rod due to this small area is given as

dε=BdAdt=Bvdx
But v=xω
dε=Bxωdx
The emf induced across the rod
ε=0lBxωdx=Bω0lxdx=Bω[x22]0l=Bω[l220]=12Bωl2

Current induced in the rod


Current induced in rod, I=εR=12Bωl2R
The power dissipated through the circuit is
P=ε2R=B2ω2l44R

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