Find the EMF in the loop as a function of time.

[ugobroncs3343]

Homework Statement

electromagnetic field

Homework Equations

E=hv

The Attempt at a Solution

I know that t is the variable and h1 and h2 I and I2 are considered given all we are doing is doing the algebra set up but not sure how to show this exactly.?

 

[Steely Dan]

Recall the definition of the induced emf,

$\text{emf} = - \frac{d\Phi}{dt},$

where the magnetic flux is defined as

$\Phi = \int \vec{B} \cdot d\vec{A}.$

Your goal is to find the flux as a function of time (clearly it is a function of time, since the area of the loop is growing with time), and then insert that into the formula for the induced emf. So it's a two step process: evaluate the integral to obtain the flux, and then take its time derivative.