# Finding average induced current in coil

**1. The problem statement, all variables and given/known data**I’m having trouble with the last part of this multiple part question, but to be honest, I’m not too sure I’ve done the initial steps correctly. Please give me feedback if I’ve screwed something up along the way (chances are I have).

A solenoid of length 20 cm is made of 5000 circular coils. It carries a steady current of 10 A. Near its center is placed a very flat and small coil with a resistance of 2.5 Ω

made of 100 circular loops, each of radius 3mm. This small coil is oriented so that its area receives the maximum magnetic flux. a switch is opened in the solenoid circuit and its current drops to zero in 15 ms. (a) What is the initial magnetic flux through the inner coil? (b) Determine the average induced emf in the small coil during the 15 ms. (c) (part c just asks about the direction of the current in the smaller coil, which I think I’ve got a handle on) (d) What is the magnitude of the average induced current in the coil?

**2. Relevant equations**

**3. The attempt at a solution**

(a) I found the magnetic field B of the solenoid, [(4∏*10^-7)(5000)(10)]/0.2 = .314159. I used that to find the flux through the inner coil- BAcosø = (.314159)(∏(3*10^-3)^2) = 8.88*10^-6 T*m^2.

(b) Average induced emf = -N *(Δflux/Δt) = -5000*(0-8.88*10^-6)/(15*10^-3) = 2.96v

(d) I’m having trouble here. A tutor at school told me to use 2.96v = -L*Δi/Δt and solve for i. However, I’d need to find inductance, and the equations I have for inductance are for solenoids, not coils. Is the given resistance of 2.5Ω for nothing, or can I use I=V/R? At this point I’m just confused.

Hopefully I made a little sense and someone can point point me down the right path. Thanks!

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