Question

Derive an expression for total emf induced in a conducting rotating rod.​

Answer 1

Answer:

Suppose the rod completes one revolution in time T. Area swept in one rotation = πL2 Change in flux in one rotation = BπL2 Induced emf =Rate of change of magnetic flux Read more on Sarthaks.com - https://www.sarthaks.com/341891/derive-expression-induced-emf-rod-rotating-uniform-magnetic-field-draw-necessary-diagram

Answer 2

Electromagnetic Force or emf induced by the rotaion or uniform motion of a conductor through the magnetic field is known as motional emf.

If we assume that the velocity is perpendicular to the magnetic field, then the charge carriers experience a force F=qvB.

Induced emf is the change in the potential difference due to a change in the magnetic flux.

Here, we are asked to derive the total emf induced in a conduction rotating rod.

Let,

The rod completes one revolution in T time.

The total area covered in one rotation = π$L^{2}$

The magnetic field is B

So, the Change in flux is Bπ$L^{2}$

We know that induced emf means a change in magnetic flux.

So,

Induced emf in a conduction rotation rod is (Change in flux)/(Time).

That will give us Bπ$L^{2}$/T

We know that T = 2π/ω

So, induced emf (e)= $\frac{1}{2} BL^{2}$ω

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