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Grade 12Top Engineering Colleges in India

A bar magnet of mass is suspended from the ceiling with amassless stringand is set into oscillations.A gold metal plate is brought close to the oscillating pendulum.The oscillations will damp due to induction of eddy currents in the metal.What happens if gold plate is replaced by a steel plate?

IRENE ANN ZACHARIAH

8 Years agoGrade 12

1 Answer

Md Mushahid

6 Years ago

Dear student,
The flux through the metal plate is changing with the speed of the magnet which you can model as:

$v(t) = \omega \times A(t)\times \cos (\omega \times t)$

$\omega =2\times \frac{\Pi }{T}$

Now the induced voltage is proportional to v(t), and thus using Ohm's Law,the induced current is proportional to v(t).
So $I-\omega \times A(t)\times\frac{\cos (\omega t)}{R}$ The power dissipated by the resistance of the metal is:

$P(t) =I^{2}\times R(\omega \times A(t))\times \cos (\omega t)^{2}\times R$

Now if R increases when you swap the plates (Steel has a higher resistance because it is not as good a conductor as gold), then P(t) will be bigger. Since this is power lost to heat, and the energy for this power comes from the kinetic energy of the magnet, the amplitude of the magnet will decrease and it will decrease more rapidly for steel than for gold

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