# induced EMF in metal loop near RC circuit

1. The problem statement, all variables and given/known data

(Challenge Problem 80, Ch33) A rectangular metal loop with 0.050 ohms resistance is placed next to one wire of the RC circuit shown in the below figure. The capacitor is charged to 20 V with the polarity shown, then the switch is closed at t = 0s.
[IMG] [/IMG]

What EMF (in V) is induced in the metal loop at t = 5.0 μs? (Assume that only the circuit wire next to the loop is close enough to produce a significant magnetic field.)

2. Relevant equations

I=(V0/R)e^(-t/RC)
dø=B . dA ?
ε = dø/dt

3. The attempt at a solution

The RC circuit discharging equation gives me the current as a function of time. I=(V0/R)e^(-t/RC)

First I tried just solving this for t= 5.0μs and got I = 6.065. Then I integrated to solve for the magnetic flux through the loop at that current and got 8.5×10^-8 T. This is where I am stuck now since I cant use ε = dø/dt to calculate the EMF with only ø and I cant differentiate this with respect to time with no time variable.

So now I’m thinking that I need to keep the time variable in my equations instead of just solving for a specific time at the beginning so i can end up with dø/dt. I calculated dI/dt and tried to use this in my integral instead of I, only now I have no idea how to solve this integral with only first year calculus. Now I’m thinking that I may have missed/overlooked something that helps to simplify this problem?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

http://ift.tt/1gbQPRL