Using Farady's law with a closed loop.

[crashdirty86]

Homework Statement

The figure below shows two circular regions R1 and R2 with radii r1 = 20.0 cm and r2 = 32.9 cm. In R1 there is a uniform magnetic field of magnitude B1 = 52.4 mT directed into the page, and in R2 there is a uniform magnetic field of magnitude B2 = 75.6 mT directed out of the page (ignore fringing). Both fields are decreasing at the rate of 11.8 mT/s. Calculate the EMF (in mV) for (a) path 1, (b) path 2, and (c) path 3.

Homework Equations

∫E ds = -dIB/dt

The Attempt at a Solution

So I began this problem by using the reformulation of Faraday's law using a closed path of an electric field and the relation to the negative time rate of change of the magnetic flux. My question of this particular problem is how to use the Right hand rule to give the appropriate signs for the voltages produced in each path.

 

[jambaugh]

I always try to remember that the induced voltage tries to produce a current which will cancel the change of the B field. (Hence magnetic levitation of superconductive objects and reflection of e-m waves by conductive surfaces..., and the basic inertial analogue behavior of inductors.)

So begin by applying the RHR for the direction of the magnetic field, that tells you the direction of the current which produced it (I use a closed fist with extended thumb RHR, fingers are current and thumb is B field but you can also use the closed fist RHR with thumb current and fingers B field.)
Then if the B field is increasing keep the direction but if decreasing reverse since this is the vector change in the B field. Now reverse once more to counter that change and that is the direction of the induced current (pushed by the induced voltage).