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COMPLETE QUESTION:
<em>When the magnetic flux through a single loop of wire increases by </em>30 Tm^2<em> , an average current of 40 A is induced in the wire. Assuming that the wire has a resistance of </em><em>2.5 ohms </em><em>, (a) over what period of time did the flux increase? (b) If the current had been only 20 A, how long would the flux increase have taken?</em>
Answer:
(a). The time period is 0.3s.
(b). The time period is 0.6s.
Explanation:
Faraday's law says that for one loop of wire the emf is
and since from Ohm's law
,
then equation (1) becomes
(a).
We are told that the change in magnetic flux is , the current induced is
, and the resistance of the wire is
; therefore, equation (2) gives
which we solve for to get:
,
which is the period of time over which the magnetic flux increased.
(b).
Now, if the current had been , then equation (2) would give
which is a longer time interval than what we got in part a, which is understandable because in part a the rate of change of flux is greater than in part b, and therefore , the current in (a) is greater than in (b).