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## Homework Statement

A square circuit of resistance R=20Ω and side ℓ = 0,2 m spins 100 times per second around an horizontal axis that splits it in two. There is an uniform magnetic field B=1T perpendicular to the position ocupied by the circuit at t=0s.

Calculate (1) the magnetic flux, (2) the inducted current and (3) the dissipated energy by Joule heating in 2 minutes

## Homework Equations

3. The Attempt at a Solution [/B]

So I had no trouble in the first 2 points, reaching:

$$\Phi_B=Bl^2 \cos(200 \pi t)$$

$$I=\frac{Bl^2 200 \pi \cos(200 \pi t)}{R}$$

Now I had trouble evaluating the energy.

I know that

$$P=RI^2$$

Taking that expression and integrating it between 0 and 120 seconds, and substituting values, I reach 1,9 kJ, which exactly half of what I was supposed to get (3.8 kJ). What am I doing wrong? Thanks!