When the magnetic flux through a single loop of wire increases by , an average current of 40 A is induced in the wire. Assuming that the wire has a resistance of , (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?

COMPLETE QUESTION:

When the magnetic flux through a single loop of wire increases by 30 Tm^2 , an average current of 40 A is induced in the wire. Assuming that the wire has a resistance of 2.5 ohms , (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?

(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).