Probably a Kirchhoff's laws problem

[Ownaginatious]

Homework Statement

Two infinitely long solenoids (seen in cross-section) thread a circuit as shown in the figure below.

http://capa.physics.mcmaster.ca/figures/sb/Graph31/sb-pic3152.png

Assume that L1 = 0.473 m, L2 = 0.473 m, H = 0.473 m, r1 = 0.112 m, r2 = 0.154 m, R1 = 6.13 Ω, R2 = 5.10 Ω and R3 = 3.28 Ω. The magnitude of B inside each is the same and is increasing at the rate of 122 T/s. What is the current in resistor R1?

Homework Equations

I believe the relevant equations to this are:

$$\epsilon$$ = $$\frac{d\oint Bda}{dt}$$

Where it can be broken down into:

$$\epsilon$$ = $$\frac{BA}{t}$$

That's how I'm trying to get the voltage for the loops.

The Attempt at a Solution

I'm trying it with the following voltage loops where the current runs up R2 and branches into the current going to R1 and R3.

So far I've set up the following voltage loops, both taken going clockwise:

(I've made the B/t equal to just G since it is given)

G*pi*$$r1^{2}$$ + R2I2 + R1I1 = 0

G*pi*$$r2^{2}$$ - R3I3 - R2I2 = 0

I2 = I1 + I3

I keep rearranging everything for I1, but it keeps coming out wrong. Could anyone perhaps tell me what I've done wrong in setting up my equations? I find this question rather confusing since we really haven't done much with induced currents in circuits.

Any help would be greatly appreciated.

Thanks!

P.S. Whoever is in charge here should consider fixing that problem where a new template is added every time I preview my post... it's very annoying.

 

[Ownaginatious]

bump...

 

[nlightner]

I would respond by saying that the problem presented is indeed a Kirchhoff's laws problem, specifically dealing with the law of electromagnetic induction. The equations that you have identified are correct and can be used to solve the problem. However, it seems that you may have made a mistake in your setup of the voltage loops. It may be helpful to draw a diagram of the circuit and label the voltage loops and currents to ensure that they are correctly set up. Additionally, you may want to double check your calculations to make sure that all units are consistent and that you are using the correct values for the given variables. It is also important to note that the direction of the induced current may depend on the direction of the changing magnetic field, which in this case is increasing. Overall, it may be helpful to approach the problem step by step and check your work at each stage to ensure accuracy.