# Shocley equation/Cyclotron motion (2Q's)

• Gogsey
In summary, the effective resistance R of a pn junction diode, as described by Shockley's equation, is dependent on the bias voltage V and approaches zero as delta V approaches 0. Additionally, in a cyclotron experiment, the charge-to-mass ratio of particles can be calculated using the equation q/m = 2V/R^2B^2, and in a mass spectrometer, this can be done using the equation q/m = -E/RB^2. In terms of the Shockley equation, as V increases, I increases exponentially and R approaches zero, while as V approaches zero, R approaches its standard value. The L'Hopital's rule may need to be applied to determine the limit of R in
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.

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?

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.

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'Hopitals (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.

## 1. What is the Shockley equation?

The Shockley equation is a mathematical formula that describes the relationship between the current and voltage in a semiconductor device. It is often used to analyze and predict the behavior of transistors and other electronic components.

## 2. How is the Shockley equation derived?

The Shockley equation is derived from the basic principles of semiconductor physics, including the movement of electrons and holes through the material. It takes into account factors such as doping concentration, temperature, and the bandgap energy of the semiconductor.

## 3. What is cyclotron motion?

Cyclotron motion is the circular motion of a charged particle in a uniform magnetic field. It occurs when the magnetic force on the particle is equal and opposite to the centripetal force needed to maintain a circular path. This phenomenon is commonly observed in particle accelerators and can also be seen in some natural processes, such as the motion of charged particles in Earth's magnetic field.

## 4. How does the cyclotron motion relate to the Shockley equation?

The Shockley equation is not directly related to cyclotron motion. However, in some cases, the Shockley equation may be used to analyze the behavior of electrons or holes in a semiconductor device subject to a magnetic field, which could exhibit cyclotron motion.

## 5. What are some real-life applications of the Shockley equation and cyclotron motion?

The Shockley equation is used extensively in the design and analysis of electronic devices, such as transistors, diodes, and integrated circuits. Cyclotron motion is important in understanding the behavior of particles in particle accelerators, as well as in the study of Earth's magnetic field and its effects on charged particles in space. It also has applications in medical imaging, such as magnetic resonance imaging (MRI).

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