Solving for a with Ma=Eq, ΔV, and m/d

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SUMMARY

The discussion focuses on deriving the acceleration of a charge \( q \) with mass \( m \) between two parallel plates separated by distance \( d \) and subjected to a potential difference \( \Delta V \). The correct approach involves using the equation \( ma = Eq \) and substituting the electric field \( E \) with the expression \( E = \Delta V / d \). The final expression for acceleration is \( a = \frac{q \Delta V}{md} \). The key takeaway is the relationship between electric field, potential difference, and plate separation.

PREREQUISITES
  • Understanding of Newton's second law (ma=F)
  • Familiarity with electric fields (E=F/q)
  • Knowledge of capacitance (C=q/V)
  • Basic principles of potential difference (ΔV) in electric fields
NEXT STEPS
  • Study the relationship between electric field and potential difference in parallel plate capacitors
  • Learn how to derive expressions for force and acceleration in electric fields
  • Explore the concept of capacitance and its implications in circuit design
  • Investigate the applications of electric fields in particle acceleration
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Students in physics, electrical engineering majors, and anyone studying electromagnetism who seeks to understand the dynamics of charged particles in electric fields.

alanwangcot
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Homework Statement
Two parallel plates are separated by a distance d and a potential difference ΔV is applied between them. Write an expression for the acceleration of a charge q with a mass m between the plates
Relevant Equations
E=F/q, C=q/V, E=1/2CV^2
Tried using ma=Eq, then subbing E for 1/2CV^2, but can't seem to be getting anywhere. How can I get to the answer which is a=qΔV/md.
 
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alanwangcot said:
Homework Statement: Two parallel plates are separated by a distance d and a potential difference ΔV is applied between them. Write an expression for the acceleration of a charge q with a mass m between the plates
Homework Equations: E=F/q, C=q/V, E=1/2CV^2

Tried using ma=Eq, then subbing E for 1/2CV^2, but can't seem to be getting anywhere. How can I get to the answer which is a=qΔV/md.
You could find the electric field.
 
ma=Eq is the right approach. The reason you aren’t getting anywhere is because you are missing an equation. If they told you the capacitance you’d be in business, but they didn’t. They gave you the plate separation d. Can you relate the Electric field to the potential and the plate separation? (hint: it’s kinda definitional)
 

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