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

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To find the induced electromotive force (emf) in a loop as a function of time, start by calculating the magnetic flux, defined as the integral of the magnetic field over the area of the loop. The area of the loop changes with time, making the flux a function of time. Use the formula for induced emf, which is the negative rate of change of magnetic flux with respect to time. This involves two steps: first, evaluate the integral to obtain the flux, and then differentiate it with respect to time to find the emf. The process requires careful algebraic manipulation to express the final result accurately.
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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.?
 

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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.
 

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