Calculating Induced EMF in a Conducting Loop with Changing Magnetic Field

[Moore65]

Here is a bonus question that I was given yesterday. I am completely at a loss of what to do. Any suggestions?

A conducting loop with a half circle of radius r=0.20m and 3 straight sections. The half circle lies in a uniform field B that is directed out of the page. The magnitude of B as a function of time is given by B(t) = 4.0t^2 + 2.0t + 3.0 where B is in Teslas and t is in seconds. An ideal battery with EMF E=2.0V is connected to the loop. The loop has a resistance of 2.0 Ohms.
a) Find the magnitude and direction of the EMF induced in the loop.

b) What is the current in the loop at t = 10 seconds?

 

[cesarsalad]

Here is a bonus question that I was given yesterday. I am completely at a loss of what to do. Any suggestions?

A conducting loop with a half circle of radius r=0.20m and 3 straight sections. The half circle lies in a uniform field B that is directed out of the page. The magnitude of B as a function of time is given by B(t) = 4.0t^2 + 2.0t + 3.0 where B is in Teslas and t is in seconds. An ideal battery with EMF E=2.0V is connected to the loop. The loop has a resistance of 2.0 Ohms.
a) Find the magnitude and direction of the EMF induced in the loop.

b) What is the current in the loop at t = 10 seconds?

just use the equation for induced emf: -dflux/dt.
flux = B(t)*area of half circle
add this emf as a function of time to the battery emf of 2.0V. I think you add, at least. they tell you the B field is directed out of the page, but they don't tell you which way the battery is connected... anyway, add 2 + (-dflux/dt) and this is your emf in the loop as a function of time. then use v = ir to calculate i(t).

 

[Moore65]

But how do I find the direction of the EMF?