# The lonely diode

A diode is characterized by its I-V curve similar to the one above.

Consider a diode whose dynamic resistance is given by

$${ r }_{ dyn }(i)=\frac { { V }_{ d } }{ { (i+\beta ) }^{ 2 }\ }\beta$$
where $$i$$ is the current and $$\beta$$ and $${ V }_{ d }$$ are characteristics of the diode.

This diode is connected from terminal to terminal with a conducting wire forming a loop. This planar loop has area $$A$$ and is kept in a magnetic field $$B$$, normal to its plane.

Find the average power dissipation (in nano-Joules) across the diode.

Given:

• $${ V }_{ d }=0.9 V$$

• $$\beta = 0.1 A$$

• $$B = { B }_{ 0 }cos(100t)$$ with $${ B }_{ 0 }= 1\mu T$$

• $$A = 1 m ^2$$

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