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 ${ B }_{ 0 }= 1\mu T$

• $A = 1 m ^2$