How is Coulomb's Law generalized for continuous charge distributions?

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SUMMARY

Coulomb's Law can be generalized for continuous charge distributions by using the formula F = k dq dq' / r^2, where F represents the force between the charge elements. In this context, the integration can be performed in either order, first over dq' or dq, to compute the total force. It is crucial to consider the vectorial nature of the force, ensuring that both magnitude and direction are accurately accounted for in the calculations.

PREREQUISITES
  • Understanding of Coulomb's Law and its application to point charges
  • Knowledge of calculus, specifically integration techniques
  • Familiarity with vector mathematics and vector fields
  • Concept of continuous charge distributions in electrostatics
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  • Study the application of integration in electrostatics for continuous charge distributions
  • Learn about vector calculus and its role in physics
  • Explore advanced topics in electrostatics, such as electric fields and potentials
  • Investigate numerical methods for calculating forces in complex charge distributions
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Students of physics, electrical engineers, and anyone interested in advanced electrostatics and the mathematical modeling of forces between continuous charge distributions.

basik156
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For calculating the force on a continuous charge distribution due to another continuous charge distribution, if F=kdqdq'/r^2 would you simply integrate first over dq' and then dq?
 
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That works, right.
 
Either dq or dq' can be integrated first.
 
basik156 said:
For calculating the force on a continuous charge distribution due to another continuous charge distribution, if F=kdqdq'/r^2 would you simply integrate first over dq' and then dq?

Don't forget to take into account the vectorial nature of F.
 

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