Electromagnetic Induction · Induction laws

A metal rod of length

L

rotates about one end at origin with a uniform angular velocity

\omega

. The magnetic field radially falls off as

B(r) = B_0e^{-\lambda r}

;

\lambda

being a positive constant. The emf induced (neglecting the centripetal force on electrons in the rod) is:

(1) $B_0\omega\left[\dfrac{1}{\lambda^2} - e^{-\lambda L}\left(\dfrac{1}{\lambda^2} + \dfrac{L}{\lambda}\right)\right]$
(2) $B_0\omega\left[\dfrac{1}{\lambda^2} + e^{-\lambda L}\left(\dfrac{1}{\lambda^2} + \dfrac{L}{\lambda}\right)\right]$
(3) $B_0\omega\left[\dfrac{4}{\lambda^2} - e^{-2\lambda L}\left(\dfrac{1}{\lambda^2} + \dfrac{2L}{\lambda}\right)\right]$
(4) $B_0\omega\left[\dfrac{3}{\lambda^2} - e^{-3\lambda L}\left(\dfrac{3}{\lambda^2} + \dfrac{L}{\lambda}\right)\right]$

We corrected a printing error in the original paper

Source printed “rotates about on end at origin”.

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