Derivation of the electric field from the potential

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SUMMARY

The discussion focuses on deriving the electric field (Ex) from the electric potential (V) for an electric dipole consisting of two equal and opposite charges separated by a distance of 2a. The potential is given by V = [ (2*(Ke)*q*x) / ((a2) - (x2)) ]. The user correctly identifies the relationship Ex = - (dV/dx) but struggles with the derivation of Ex = - 2*(Ke)*q * [ { (a2) + (x2) } / { ( (a2) - (x2))2 } ]. The suggestion to apply the quotient rule for differentiation is emphasized as a key step in solving the problem.

PREREQUISITES
  • Understanding of electric dipoles and their properties
  • Familiarity with electric potential (V) and electric field (E)
  • Knowledge of calculus, specifically differentiation and the quotient rule
  • Basic understanding of electrostatics and Coulomb's law
NEXT STEPS
  • Practice deriving electric fields from potentials using the quotient rule
  • Study the concept of electric dipoles in more detail
  • Explore applications of electric fields in electrostatics
  • Review calculus techniques relevant to physics problems
USEFUL FOR

Students preparing for physics exams, particularly those studying electrostatics and electric fields, as well as educators seeking to clarify concepts related to electric dipoles and their derivations.

stargirl22
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I am studying for a test and i can't figure out for the life of me how my book derived the solution for this problem I know it has to be basic i just don't see it...

An electric dipole consists of two charges of equal magnitude and opposite sign separated by a distance 2a... The dipole is along the x-axis and is centered at the origin.
calculate V and Ex if point P is located anywhere between the two charges.

I understand the concept of this, and have calculated V, which is [ (2*(Ke)*q*x) / ((a^2) - (x^2)) ] and i know how to start the problem of Ex...

Ex = - (dV/dx) = - [ (2*(Ke)*q*x) / ( (a^2) - (x^2) ) ...

But I can't remember or figure out for the life of me how they got

= - 2*(Ke)*q * [ { (a^2) + (x^2) } / { ( (a^2)-(x^2) )^2 } ]

Can Anyone please help? :D
 
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try using the quotient rule for the derivation! You will get it!
 

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