Solve Equation (1) to Get Equation (2): The Depletion Voltage & Electric Field

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SUMMARY

The discussion focuses on deriving Equation (2) from Equation (1) using algebraic manipulation in the context of electric fields and depletion voltage. Participants confirm that letting the electric field (E) equal zero at radius r1 allows for solving the potential (V). The symbols Vd (depletion voltage) and Vo (potential difference across the junction) are defined, clarifying their roles in the equations. The conclusion emphasizes the importance of correct sign conventions in the terms of the equations.

PREREQUISITES
  • Understanding of electric fields and their mathematical representation
  • Familiarity with algebraic manipulation of equations
  • Knowledge of depletion voltage and its significance in semiconductor physics
  • Basic concepts of potential difference in electrical circuits
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  • Study the derivation of electric field equations in semiconductor physics
  • Learn about the significance of depletion voltage (Vd) in junctions
  • Research algebraic techniques for manipulating complex equations
  • Explore the implications of potential difference (Vo) in electrical engineering applications
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Students and professionals in electrical engineering, physicists studying semiconductor behavior, and anyone interested in the mathematical foundations of electric fields and depletion voltage.

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The electric field
upload_2016-3-22_18-43-23.png
...(1)

by saying that
upload_2016-3-22_18-47-49.png
...(2)I tried to integrate equation (1) from r2 to r1 but could not get equation(2).

Any suggesting.

Thanks
 
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Looks like you should be able to get (2) from (1) with just algebraic manipulation. Did you try letting ##E = 0## in (1) when ##r = r_1##and then solving for ## V##?

However, I get that (2) should have a positive sign for the last term.

Can you define the symbols ##V_d## and ##V_o## that occur in (1) and (2)?
 
TSny said:
Looks like you should be able to get (2) from (1) with just algebraic manipulation. Did you try letting ##E = 0## in (1) when ##r = r_1##and then solving for ## V##?

However, I get that (2) should have a positive sign for the last term.

Can you define the symbols ##V_d## and ##V_o## that occur in (1) and (2)?
Thanks for your prompt respond.

Vo is the difference in potential across the junction
Vd is the depletion voltage
Also for equation (1) the second term has a positive sign.
After doing some algebra i end up with equation (2).

Thanks for the help.
 
Last edited:

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