Shocley equation/Cyclotron motion (2Q's)

[Gogsey]

What is the effective resistance R of a pn junction diode that obeys Shockley’s equation, as a function of the bias voltage V ? What is the resistance in the limit delta V approaches 0?

I know the shockley equation, but how does reistivity relate to it? I'm assuming you can substitute it in the quation relating it to current, but I'm not sure of the espression. Last parts ok to. Resistance should go to zero, right?

Then he turned off the electric field, and measured the radius of curvature R of the beam, as deflected by the magnetic field alone. What is the charge-to-mass ratio q/m of the particles in terms of E, B and R?

This is to do with a cyclotron, initially with equal magnetic and electric fields, such that the net force was zero, and the electron only went perfectry striaght perpendicular to the forces. Then he turns off the electric field. This is like a mass spectrometer.

I know tha R=mv/qB, so there's the relation of R and B, but how does E fit into all of this. E=qV, but I can't see anyway of fitting this in, sine we need the q for the ratio q/m.

 

[Gogsey]

Ok, quick update. I have the equation q/m = 2V/R^2B^2, so now do I have to integrate Voltage over the area of the semicircle?

 

[Gogsey]

Now I have that from mag F = Lec F to get a velocity using the veloctiy selector, we
v = -E/B. Subbing this iunto r=mv/qB, we get q/m = -E/RB^2. Not entirely sure about this but I have something in terms of R, B and E. Plus for the next part, we are only given E, B and R to calculate the ratio.

 

[Gogsey]

Ok, for the Shockley equation question, i have as V increases, I increases exponentially. From R=V/I, sice I increases much faster than V, R approaches zero.

Now for the part where V goes to zero, the whole e function goes to 1, and then 1-1 is zero, so I becomes zero. Then from R=V/I we have 0/0. Now I was taught that this is not just zero, since we need to know which one approaches zero faster using l'hospital's (not sure if this is how you spell it) rule. Does this apply here though?

Also from the V vs I graph of Sockley's equation we see that the slope,1/R becomes less steep and approaches zero, which would mean the resistance is getting bigger, and approaching its standard value.