Find v(z) given volume charge density

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SUMMARY

The discussion focuses on calculating the electric potential v(z) in a parallel plate capacitor with a volume charge density defined as ρ_v = ρ_o*sin(pi*z/2*d). The solution involves integrating the charge density to find the electric potential, resulting in the equation v(z) = -ρ_o*(2d/pi)^2*sin(pi*z/2*d) + Az + B. Participants emphasized the necessity of using definite integrals to determine the integration constants and pointed out the omission of the permittivity constant ε0 in the calculations.

PREREQUISITES
  • Understanding of electric potential and charge density concepts
  • Familiarity with calculus, specifically integration techniques
  • Knowledge of parallel plate capacitor configurations
  • Basic principles of electrostatics, including the role of ε0
NEXT STEPS
  • Review integration techniques for electric potential calculations
  • Study the role of permittivity (ε0) in electrostatic equations
  • Explore the derivation of electric fields in parallel plate capacitors
  • Investigate the effects of varying charge densities on electric potential
USEFUL FOR

Students in physics or electrical engineering, particularly those studying electrostatics and capacitor behavior, will benefit from this discussion.

derek l

Homework Statement


Consider the parallel plate capacitor(no figure). The capacitor plates have a separation distance d in the z-direction. The volume charge density is given by ρ_v. Find v(z).

Homework Equations


ρ_v = ρ_o*sin(pi*z/2*d)

The Attempt at a Solution


[/B]
∫(ρ_vdz) = -ρ_o*2d/pi*cos(pi*z/2*d) +A= dv/dz

∫dv/dz = -ρ_o*(2d/pi)^2*sin(pi*z/2*d) +Az + B = v(z)
 
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You need to consider definite integrals so that the integration constants can be defined. What are your limits of integration? Also, it looks like you are missing an ε0 somewhere.
 

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